If you mean in addition to a properly constructed and functioning fruiting chamber - then yes (for the most part).

Avoid closets and close spaces.

FAE is Fresh Air Exchange... what we're talking about is swapping out the air in the fruiting chamber for fresh air. It needs happen many times a day.

For anyone serious about improving their fruiting plan, I highly recommend reading up on the concept. There are many ways to get there, some simple and some complex. For the OP's Shotgun fruiting chamber... I'd drill more holes 1/4" every 2" on all 6 sides of the tub. Putting a fan directly on it will probably beat the RH down to much... but a fan in a corner of the room moving air gently (like you mention above) will help.