You can't possibly play worse on a good quality instrument, but you definitely can play badly on a low quality instrument that has various issues, and it is those issues that might just kick you out of learning guitar all together.
A high quality instrument that is well made and intended for professional performance, and is set up correctly, will do its best to your abilities and you will grow into it over time. This is what happened to me with another instrument I learned to play. As a result, I aimed for the best guitar I could afford.
I was lucky this time around in that I found a used ESP M-II which was just a tad over $700 and yet it is an immaculate instrument. It looks to me like it's never been played before.
It feels so comfortable and well balanced, that I didn't want to put it down when I gave it a bit of a try today. Alas it is not tuned, and because it has Rose Floyd double locking tremolo, it is beyond my abilities at this stage to tune. So, I'm taking it to a technician next week for new strings and tuning. When that is done, I'm off to a flying start to learning the electric guitar on one of the best instruments out there. If it sounds crap, then I know it's me, and not the instrument :)
Always get the best you can afford. It's definitely worth it.
The accidental guitarist.