Yes; if the acceleration from gravity exceeds the rocket's thrust-to-mass ratio, the rocket cannot make any upward progress against gravity. The best engine listed on the Wikipedia article was the Merlin 1D with 180.1 gravities, so g ≥ 1767 meters per square second would suffice to keep it on the ground, less if you account for the fuel tanks and such.
You can always make a mass driver system (which is not limited by the rocket equation), but given how insanely hard it is at our own gravity, it would be more insanely difficult at a few times great g.
So there's definitely a quite low maximum gravity allowing practical space access.
The ability to launch from the surface is proof of it's finiteness.
As a corralary it should be finite as long as you're not inside a blackhole.
It should be asymptotic up to that point. Mathematically infinite at the horizon and then completely unbounded inside it (in the sense that it converges to infinity versus not converging at all ( see a "flat" universe versus hyperbolic)).