Hello! SynthEngine is pure GML and runs on the same thread that your game's logic runs, and generating audio buffer data is an expensive job. Using SynthEngine to power the music in your game is definitely something that can be done, but the music it can produce (without causing performance issues) will be limited. For example, having only one or two oscillators should not cause issues. See this example video of me playing a small tune with a single oscillator and 4 note polyphony:
If you are open to sharing your project with me (or an isolated example project) I'd be happy to take a look at it for you and see if I can help.
One avenue of exploration may be to have some parts of your music be from an audio asset and some parts (like a melody line or lead voicing) be generated by SynthEngine. Keeping them in sync represents an upfront challenge, but it should be possible.