Does an Electrical Metallic Tube (EMT) Inside Corner Pull Elbow count towards the 360° total bends?

Only if you pull from there

If you're not actually using it to pull... then you can't use it at all. This turn is far too tight to pull around. It will simply tear the wire.

If you're actually going to use it to pull... then this not only doesn't count toward your 360, it resets your 360! Say you have

 ===90 sweep===90 sweep===this thing===90 sweep===

That isn't 360 degrees, that's not even 270. It's a 180 section followed by a 90.

However, a inside corner is a BAD place to pull.

And this thing, which is a pulling elbow with side access, is a red flag for a thing you should really, really try to avoid.

An inside corner should be a sweep.

The better place for conduit bodies and pulling elbows is outside corners. In those locations, the normal lids will suffice.

Remember, you build the conduit empty. Only pull after it's finished.

This business about 360 degrees and access points isn't some arbitrary rule you must memorize and do for no reason. It's there specifically because conduit must be pullable. (or else it isn't conduit). The litmus test of "pullable" is that you actually do pull the wires into it.

Code requires you build (and finish) the physical conduit work before you pull a single wire. That pretty much "holds your feet to the fire" to build conduit properly.