Well, yes, that's how convolution reverbs work. Except I've never seen anything that would allow users to record a reverb with conventional hardware and without any elaborate setups.

Also, there is more to reverb than just impulse response. A more sophisticated reverb simulator would map out the space and allow you to choose where the "listener" and the source are located in that environment.

The nearby comment about moving obstructions is on-point as well.

There is ample space for application of machine learning here.

Reverb of a static room at a point is as simple as that. Rooms with moving obstructions, with moving noise generators, at moving points, that's harder.

You really might not even need to make a great impulse... you can probably get away with recording response to a series of "known signals" (e.g. chirp signals played back over a known loudspeaker), and then determining the impulse response from that, and applying that (via convolution) to your actual signal of interest.