Do snapshots only work with AR turned on?

Solution 1:

Yes you have to take a snapshot using your phones camera, it has to be of a captured Pokemon. It doesn't, however, require you to use AR+ which is useful. From the article linked below:

Taking a snapshot of a Dratini is a bit more tricky as you have to catch a Dratini first. When you've caught one, just click on the camera icon at the top of the screen to take a snapshot of it. Or if you don't want to go out and catch a new Pokemon and already have a Dratini, select it in your Pokemon list and click the camera icon at the top right-hand corner. The little fella will appear in AR, and then you just tap the camera icon again to take a snapshot of it.

Sources: I've been playing the game for years and related articles available online.

Jump Start Research

As a side note from what I entered in the comments, the Snap Shot feature is the only current way (as of September 2019) to obtain a Smeargle. It will randomly photo bomb your picture (appearing in the bottom corner) and then be catch-able in the game world.