I think overall the approach is ok, but I have the feeling there are more computations done than necessary. How about changing BKE_nlastrip_intersects_frame() to float BKE_nlastrip_distance_to_frame(strip, frame) that returns the actual distance of the frame number to the strip itself? I'm thinking something like (untested and badly formatted):

float BKE_nlastrip_distance_to_frame(const NlaStrip *strip, const float timeline_frame) {
  if (timeline_frame < strip->start) return strip->start - timeline_frame;
  if (strip->end < timeline_frame) return timeline_frame - strip->end;
  return 0.0f;
}

You can then use this distance to find the closest, and when distance == 0.0f you're sure that it intersects -- no further processing necessary.

This also provides a better separation of abstraction -- rather than having the loop itself doing some computations and deferring others to a separate function, with my suggested approach only one function is responsible for computing that distance.

As a request for future passes, before submitting please do a pass to verify that all parameter and local variables that can be const actually are declared as such.

... my intention was very quick and simple fix
In VSE I pay quite a bit of attention to form these comparisons ...

From the in-line comments, I get the impression that you're more careful with the VSE code than with the NLA code. That's a bit of a dubious attitude, and I hope I'm interpreting things incorrectly.

Anyway, the patch looks almost good to go. Just a little nag about the documentation of BKE_nlastrip_distance_to_frame().