You can assume that, if the machine runs out of memory, that someone comes along and installs another gigabyte and sets it going again. Predicting whether programs will halt under those conditions is exactly the same as if they really had an infinite tape.

It's a bit tricky with real programs because eventually you might expect you'd run out of address space, so you might have to relax constraints and say that at least some integer types don't have a defined maximum value, or stuff like that.