Hi azgini - thanks for the post, and welcome to the Forum!
Not a silly question at all! In fact, you're smart to double-check any and every possible thing that could cause a problem on test day, as the last thing you want is a distraction (or worse).
I suspect a mouth guard is entirely fine and would be allowed by the proctors, as it seems to be a medical device no different than eyeglasses or a knee brace. However, your safest bet is to contact LSAC directly—either by phone or in writing—and have this confirmed, and if you can get that confirmation in writing via email then print it out and take it with you on test day to show any proctor that hassles you. That way you're 100% in the clear, and can focus your full attention on the test itself!
And since I imagine you're not the only one out there with this question/concern, post back here with an update (if you can) when you get confirmation one way or the other from LSAC
Jon Denning
PowerScore Test Preparation
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