Guess that would depend if it is a hardware of software issue.
Have you tried a factory reset? Probably a pain, but might be a way test it.
You have an HTC warranty, so it may be wise to avoid rooting when you have a real issue that is not normal.
Honestly, I think it could help, but under your circumstances I would be hesistant. Especially if you have a back-up phone and you can send your phone into HTC with limited annoyance.
Just my 2 cents, but really seems risky to root a phone that may have legitimate problems(unless you are confident its a pure software issue).