Can "while" be followed by "will"?

Looking up while in any good dictionary tells you that it's a conjunction that connects two events, both taking place in the present or in the past.

Examples:

While I'm working on my PC, I do not want any distraction.

We were watching the TV, while the slanging match was going on in the other room.

While he was walking, he often seemed to reel.

It would thus be seen that tenses as such pose no encumbrance to using while to carry out its primary function as conjunction— to introduce subordinate clauses.

But as a note of caution, and as has been pointed out by @Lawrence, while in OP's first sentence, instead of faithfully conveying the simultaneity of two events as is apparently the intended usage of the word, seems to suggest its other meaning— whereas: when on the other hand. And this could sometimes be potentially misleading.

There's no formal future tense in English, although the future may be referred to by using will.

"I will go tomorrow" expresses at least an intention; but that can also be expressed by "I am going tomorrow" or even "I go tomorrow".

british-english [What follows may not apply to other versions]

While (= "at the same time as") does not license the will form of expressing the future. If you use while with will, as you propose, then while always has the meaning "although". [Note: this is a shibboleth for non-native speakers: many languages do license — if not insist upon — a future "tense" with while which cannot simply be translated word-for-word.]

For the "future tense" with while, you need to use a different form of the verb; this might be present continuous or simple present:

While the engineers give a press conference, the inspection team will investigate the accident scene.
While the engineers are giving a press conference, the inspection team will investigate the accident scene.

Using will give for the engineers' part in the process always makes while mean something similar to "although":

While the engineers will give a press conference, the inspection team will investigate the accident scene.
Although it is the engineers who will give a press conference, the inspection team will investigate the accident scene.
The engineers will give a press conference, but the inspection team will investigate the accident scene.

Neither of those alternatives has quite the same meaning as the while version.

From CGEL, 15.28 (Same time) p. 1083

In the two copies above, among the material provided so as to situate the discussion more precisely, is directly relevant the following sentence.

• While and the less frequent whilst require that their clause must be durative , but the matrix clause need not be.

Of course, the answer to the question depends on what is meant by the term "durative clause". It is not a term that you find often in grammatical text. However, the concept of durative verb is clearly defined in this reference: flesl.net grammar glossary; moreover, there is a part in it that indicates, although implicitly, what is meant by "durative clause"; the part showing it has been copied below for convenience.

The revealing sentence

• When a durative verb is put into a progressive tense, the meaning is that an event is (or was) going on over a period of time. It follows that not any tense (aspect) of a durative verb necessarily yields a durative meaning, or in other words a durative clause.

Notice that "to give" is a durative verb. The necessity of this durative construction is corroborated by the fact that if there is doubt about the sentence in question (rightly so) there is no doubt for the following variant: it is correct and carries the idea of "same time" (not that of concession).

• While the engineers will be giving a press conference, the inspection team will investigate the accident scene.

As a conclusion, it can be said that if a verb form with "will" in a clause introduced by "while" is in a continuous tense it does confer the notion of "same time".

There are two possible meanings here, and the differences are subtle. If the person making the statement is essentially setting a schedule, "will" would not be used.

"While the engineers give a press conference, the inspection team will investigate the accident scene."

That is, the engineers will give a press conference at the same time that the inspection team investigates the scene.

If the speaker is dealing with a more general division of responsibility, and is prescribing roles or functions of the two teams, "will" could be used.

"While the engineers will give a press conference, the inspection team will investigate the accident scene."

In this case the speaker is telling the engineers to give the press conference, and the inspection team to inspect the wreckage. It also suggests that either group could give the press conference.

The distinction is between uses of the word "while". If it is used to establish a future time, there is no need for "will", which would normally be used to do that.

The other use of "while" is to establish preference between choices, as in, "While I like both cake and pie, I'll have the pie for dessert." In this case it would be used to tell each team what they will do, while acknowledging that either could give the press conference. The alternative would be that both teams give the press conference, since presumably the engineers are not as good at investigation as the inspection team.