This is the modal verb
may being used to denote concession, EL.
It means "allowing the possibility that these responses to tension and over-tiredness are useful".
It's used when one doesn't want to argue too strenuously on one point, so they admit that it
may be true. This concession is meant to forestall/stop the person, whose opinion it is, from interrupting a further point one wants to make.
A: It's supposed to rain tomorrow.
B: While it may well rain tomorrow, I don't think we should let that spoil the plans for the picnic. We can always move it indoors.
Kinda a dumb example but I hope you get the point.
Here are a ton of examples from a google search for,
"though it may be",
that you can read to further enhance your understanding. Come back with more questions if you feel the need.
" though it may be" - Google Search