This is kind of a 2 part question. The first part, about FreeRTOS really revolves around the meaning of the word "support". A salesman would of course say yes, if any port of FreeRTOS can run on Teensy, then of course it's "supported".
But the honest reality of "supported", meaning at least some reasonably large subset of the code you'll find for Teensy actually works with FreeRTOS, or meaning that you'll get good answers from us here on this forum, then no. Hardly any of the existing libraries and non-trivial programs are thread safe, not to mentioned designed to integrate well with multi-threaded FreeRTOS projects. Hardly anyone here really uses FreeRTOS. So while there may be ports that can at least do some trivial things, for all practical purposes FreeRTOS isn't really a viable path, unless you want your project to largely about fiddling with FreeRTOS.
The good news is I have a much better answer to the other half of your question. Well, Theremingenieur already mentioned the audio library. It's comes with its own multi-tier interrupt scheme that allows for your Arduino code, and most other libraries which also need interrupts, to run while the audio is playing. Not a full RTOS, but it does solve the concurrency issue quite well and gives good compatibility with most other libraries, even ones needed fast interrupt response. There's a detailed
tutorial for the audio library which tries to explain this with some hands-on examples in parts 1-4 and 1-5 (pages 5-7 of the PDF manual).
I'd highly recommend going through the tutorial material. The PDF is 31 pages. The ideal way is to print the whole thing and sit down for 3-4 hours with the hardware and actually do all the parts. Or you can watch the 45 minute video of me & Alysia doing a full walkthrough. Much like video game walkthroughs, you can quickly see everything happen and get a pretty good idea, but actually playing it all yourself is the way to get the real experience.