Yes, any Cursor sub includes a separate tier of usage for Cursor/SpaceX first party models separate from usage of third party models.

I have a $20 Cursor sub still personally and would say that the usage for Grok models is much higher than what $20 gets you with Anthropic. I can't speak for the $100 plan but I would assume it scales similarly.

I rarely run out of my usage monthly even with the $20 plan.

I'm on the $20 plan too and the only time I run over is if I'm using Opus (or probably other third-party models). Grok and Composer seem nearly free at this point. Cursor also gave me a $100 credit for Grok after 81% of my usage was on TP models. I don't think Grok 4.6 is quite at the level of Opus 5, but it's close and so much faster (and less chatty).