Yes, basic aerobatics are totally possible. You'll be doing loops, rolls, Immelmann's, split-s's, figure-8's and stall turns before you know it. With a bit of practise you'll even be flying inverted, although the high dihedral on the wings of trainers will keep trying to flip you up the right way again and the flat bottomed airfoil design of most trainers will mean that you're flying more on the elevator than the wing . I even know people who have learned to perform more advanced aerobatics like rolling circles using their trainers!

Basic answer is yes, they can do quite a wide range of aerobatic manouvers. They're not going to do them as elegantly as a plane designed for aerobatic flight, and in quite a few cases it's actually going to be harder to perform the manouvers using your trainer, but you're going to have plenty of scope for learning.

Having said that of course, when I was starting out with my trainer just keeping the thing in the air and learning how to get it onto the ground in one piece were plenty for me!

Have fun,
Neil.