What happens if a psykers psi rating falls below zero due to an untouchables presence?

TLDR the psyker is screwed.

First of all, does Rogue Trader actually have an untouchable package? I only see it in the Radical's Handbook and that's a Dark Heresy source.

Rogue Trader mentions it in a table on page 172:

Untouchables: An Untouchable reduces the Psy Rating of any psyker (within 5 metres) by 5. All other rules for Untouchables are unchanged.

The Rogue Trader rulebook doesn't mention any specific issues with negative psy rating, and neither does the errata.

But keep in mind a few things:

• You add psy rating x5 to your focus power test, and with a negative effective psy rating that's a penalty. You are much more likely to fail.
• Most of the powers will have no effect with psy rating of zero or lower because it acts as a multiplier on a base figure for range or damage.

Personally, I'd rule that one needs at least 1 in effective psy rating to actually manifest a power, and that trying to manifest a power while at zero or less effective psy rating leads to a psychic phenomena.

Note that effective psy rating can be boosted by a push back to positive numbers, so there is still hope for a psyker near the untouchable.