There wasn't an option for unsure so I didn't vote. It sounds like your head is in the right place so I would tend to say "yes" to the question. But I agree that you should maybe ride more than just this one horse before making a decision. My horse was a free OTTB from my grandfather and the only thing that has saved me is that he is a very laid back specimen of his breed. I love him to death but he's most likely NOT the horse I would have bought if I had been shopping. But now I love him, he's such a pocket horse, and can't stand to get rid of him. Anyway... listen to your trainer but maybe look around a little before taking a "free" horse.
Riding: The art of keeping a horse between you and the ground. ~Author Unknown