Is it possible to have two points, point A and point B, on plane X, and not have a line that connects them?
No it's impossible.
The definition of a LINE on an axe is a COLLECTION OF DOTS THAT CONNECTS POINT A (DOT) TO POINT B.
2 points define a line. 3 points not on the same line define a plane. Etc.
no. it is impossible---2 points ALWAYS make a line.