Short answer: Yes - up to a point
Ignoring things like Kopi Luwak etc, there is a cost associated with growing, harvesting and transporting arabica beans in a timely manner, roasting them while they're fresh, and getting them to somewhere you can buy them.
If you go below this price, corners will be cut. You may get cheaper robusta beans, or a mix. You will get older, staler beans. You will get the poor end of the harvest.
However, go above that price and you're needlessly spending extra cash. You're now spending on marketing for the people you're buying it from. You're paying for a fancier bag, better branding etc. This may actually make it taste bette - psychology is a powerful thing, but the beans you're getting won't be significantly different.
The problem is, this magic price-point is impossible to find, fluctuates wildly, and it's in the interests of suppliers to obfusticate it as much as possible.
My advice would be to try a variety of coffees that you can afford and find one you like.