I'm just gonna be working on a natural minor for now. I'm wondering if it's still possible to jam with people if they are on the harmonic or melodic scales of the same key, or will it sound wrong?
There isn't really an easy answer to this question.
The natural, harmonic and melodic minor scales are very closely related and are a part of a family of related scales and modes from which borrowing and interchange is exceedingly common. You can expect, therefore, that for the most part it will be okay if you simply play in the natural minor scale if the underlying progression you're playing over heavily suggests the harmonic minor scale (note that the melodic minor scale is so named for its relatively uninteresting harmonic properties).
You are going to miss out on some pretty important cadences, however, and only playing in a scale that is closely related to but not exactly the same as the underlying harmony is generally pretty problematic due to your inability to relate properly to the primary V7-i cadence of the key.