Does this sentence still make sense?

Hmmm, it's hard to know if this fits with the narration without more context. My first reaction is that such a description is unusual in third/past, but technically I don't think it's wrong and is perhaps a matter of style. Do we get this close to his thoughts elsewhere? If other such instances were more in the style of "He hoped he would hear her bow in time to respond" or "He wondered if he would hear her bow in time to respond" then this would be awkward.

There's a lot of variation in POV, and as Chris P stated, it's all about consistency of style.

I usually write in close third, and so consider: 'he caught himself wondering' to be filtering, something that pulls me away from the immediacy of the action, and would put it this way:
He smiled warily as he turned away. Would he hear her draw and release in time to avoid an arrow in his back?

Technically, yes, it makes sense but it feels like an early draft sentence.

H7TM4N said:

Would he hear her bow in time, he caught himself wondering, to jump out the way of any arrows possibly heading for his back?

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I have a few thoughts. I don't think any person can jump out of the way of an arrow under these circumstances, so that thought feels a bit dim-witted to me. And, she will only fire one arrow at him, at a time, so the plural is odd. I feel the tag would better placed elsewhere. And I think if you are going to use an adverb, reach for a surprising one. Play with them and find one that gives you more joy than 'possibly heading.' Or drop the adverb altogether. My first revision of that sentence for my own writing (which is not your writing, and should not be) would adjust all of those details.

He caught himself wondering if he'd hear her bow in time. Would he even know if an arrow was (happily sailing toward)/(madly careening toward)/(silently speeding toward) his back?

A brief aside - one of my Karate Instructors, Kyoshi Jim Mather, could catch arrows at about 100 feet distance. That said, he was prepared, saw the arrow launched, and knew where it was headed. At close range, I doubt anyone could hear the release and get out of the way in time - there would have to be some way to anticipate in order to survive.

Arrow catcher video

I say ditch the 'he caught himself wondering' ... that just makes the sentence hard to read. I think indianroads' suggestion is very good.

The existing sentence seems too long and over-explanatory to me. Isn't it obvious to the reader that there's a risk turning his back on someone with a bow and whom he suspects might do him some harm.

Don't know what sentence covers his turning his back on whoever it is, but have you considered just adding a simple - Was that a wise move? or similar.

Or add nothing, and have him walk away 'alert for any indication that turning his back on her had been a bad idea'.

Also:

Would he hear her bow in time

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Bows don't make any noise.