Yes, you can use your spinner with console emulators, but most don't have the basic functionality of the MAME emulator. Often, that means you won't be able to dial in the sensitivity or reverse the axis, as well as not getting multiplayer functionality in the rare case of games like Arkanoid Revenge of Doh Doh it Again on SNES that support two mice, since most emulators are locked to X-axis mouse functionality.
I haven't tried Atari paddle games yet, but I'd be surprised if you could get 2-4 player Pong or Warlords running on a 2600 emulator. I was recently gifted an Atari 2600. I haven't played paddle games on the original console since the early 80's was surprised to find that the paddles have large deadzones at the ends of the rotation and that they seem to use only maybe 90 degrees of the rotation, but I have yet to test any emulator to see how they handle paddle emulation.
My first player TurboTwist 2 spinner works for Master System, NES, and SNES games, but generally the high spinner resolution (same as the SpinTrak) makes the paddle control very twitchy, so you find yourself making micro-movements and it isn't that great.
Only one Playstation emulator I tried had mouse support for the rotary option in Tempest X, but the axis was reversed for my spinner, as it's emulation a Playstation mouse. I reported the issue on Github, but I don't think it's high on the developer's priority list.
BigPemu is a recently released emulator for Atari Jaguar and runs amazingly well. This one was frustrating because he claims to support rotary controller functionality in Tempest 2000, but it seems to be completely non-functional as there is no way to map anything to the rotary axis and of course no sensitivity or axis reversal option. Again, I reported the problem, but I just don't think that spinner support is something many console emulation developers know and/or care about.