Does the UA invocation Improved Pact Weapon work with Elemental Weapon?

By RAW: For the Unearthed Arcana version, probably no, because of the dubious "+1 weapon" reference. The argument cruxes on claiming a "+1 weapon" to be a defined term that only appears under magical weapon definitions which refers to such a weapon as a magic weapon.

For the officially released version in Xanathar's Guide to Everything, Yes you can cast Elemental Weapon on your improved pact weapon. Improved Pact Weapon doesn't make your pact weapon magical. Though it should be noted you likely should only get the +1 to damage from IPW and not the extra +1 to attack after elemental weapon makes it magical and gives it +1 to attack. Due to the ambiguous wording, it could also be interpreted that you get neither the +1 to attack or the +1 to damage from IPW, or that you get both the +1 to attack and damage from IPW (+2 to attack total with Elemental Weapon)

Elemental Weapon reads:

A nonmagical weapon you touch becomes a magic weapon. Choose one of the following damage types: acid, cold, fire, lightning, or thunder. For the duration, the weapon has a +1 bonus to attack rolls and deals an extra 1d4 damage of the chosen type when it hits.

Ergo, after casting it on your pact weapon, your pact weapon would become a magic weapon with +1 bonus to attack rolls, (but not +1 to damage rolls)

Here's what Improved Pact Weapon says in the Xanathar's Guide to Everything book (p. 57):

Prerequisite: Pact of the Blade feature

You can use any weapon you summon with your Pact of the Blade feature as a spellcasting focus for your warlock spells.

In addition, the weapon gains a +1 bonus to its attack and damage rolls, unless it is a magic weapon that already has a bonus to those rolls.

Finally, the weapon you conjure can be a shortbow, longbow, light crossbow, or heavy crossbow.

So it is not clear if this means if it already has a bonus to either or of those rolls or to both of those rolls or if the +1 would apply only to the rolls it doesn't already have the bonus to. Further complication comes from the use of the conditional already. It could be argued the weapon only got the +1 bonus to attack rolls from elemental weapon after the IPW bonus was previously granted when it wasn't magical and had no bonuses and that after casting elemental weapon it doesn't "already" have the bonus, it just got the bonus, so that conditional is not satisfied, it would only be checked when you first make the pact weapon.

The Unearthed Arcana version read:

Any weapon you create using your Pact of the Blade feature is a +1 weapon. This invocation doesn’t affect a magic weapon you transformed into your pact weapon.

For the official release, they worded it better and added the 1st and 3rd abilities.

As it's officially released, I don't see how improved pact weapon has any bearing in whether or not a pact weapon is magical. It should be completely irrelevant. There is no reference to magic, being magical or nonmagical, or any way that magic is implicated.

A +1 bonus to attack and damage does come a lot with magic weapons, but not all, or I'd wager not even most magical weapons. Even if all magical weapons had +1 attack and damage that doesn't mean a weapon with +1 attack and damage is magical. If Q then P does not grant if P then Q, that's a very common logical fallacy of affirming the consequent.

If a special weapon was forged with lighter metal and a sharper blade that gave it +1/+1 it wouldn't have to be magical. If something heals for 2d4+2 it doesn't have to be a healing potion.

Further, there's examples like Magic Weapon which reads:

You touch a nonmagical weapon. Until the spell ends, that weapon becomes a magic weapon with a +1 bonus to Attack rolls and Damage Rolls.

If the +1 bonus to attack rolls and damage rolls in of itself made the weapon magical or implied it was magical they wouldn't have also written "that weapon becomes a magic weapon"

Further example for the intentions of the writers comes from later UA release that included Superior Pact Weapon

Prerequisite: 9th level, Pact of the Blade feature You can use any weapon you summon with your Pact of the Blade feature as a spellcasting focus for your warlock spells.

In addition, the weapon counts as a magic weapon with a +2 bonus to its attack and damage rolls, unless it is already a magic weapon that you transformed into your pact weapon.

This last clause "unless it is already a magic weapon that you transformed into your pact weapon" I believe was the intention on IPW with the conditional "already". Thus, for RAI, I would argue Elemental Weapon plus IPW not only works, but would give you best possible interpreted outcome outcome of +2 to attack and +1 to damage and the 1d4 of elemental damage.

So then your just left with is the pact weapon magical to begin with, which by RAW, I would say very clearly no, it isn't magical. It never says it is, and it virtually expressly says that isn't:

This weapon counts as magical for the purpose of overcoming resistance and immunity to nonmagical attacks and damage.

A weapon doesn’t need to count as magical unless it isn’t magical. Ergo, a Pact Weapon is intrinsically a nonmagical weapon. (With the exception being if you convert an already magical weapon into a Pact Weapon)

Since we are told over and over that if something is meant to be in the rules, the rules will say so, we know that a Pact Weapon -only- counts as magical “for the purpose of overcoming resistance and immunity to nonmagical attacks and damage”.

Mike Mearls tends to agree.

If they wanted it to be magical they could have more easily said it was magical instead of "This weapon counts as magical for the purpose of overcoming resistance and immunity to nonmagical attacks and damage."

RAI however I think is messy and you'd see some split among DMs with reasonable claims to both sides; I think the sides of pact weapon and IPW not being magical are much stronger, but they don't write their intention very well. Then to be more controversial they also seemed to intend hexblades to cast this spell by adding it to their expanded spell list and intended pact of the blade and IPW to be used most commonly with hexblade. They seemed to be intending you to cast EW on IPW but were very unclear in how interpret what should follow afterwards, what a mess.

The Improved Pact Weapon eldritch invocation from that UA does indeed make your weapon a magical weapon:

Any weapon you create using your Pact of the Blade feature is a +1 weapon.

A +1 weapon is a specific magic item from the DMG (pg. 213). If that's insufficient proof of magicality, the description of +1 weapons specifies that:

You have a +1 bonus to attack and damage rolls made with this magic weapon.

So if you have the UA Improved Pact Weapon invocation, your Pact Weapon is very much magical and therefore can't have elemental weapon cast on it.