My son, who is cleft-affected, has tubes to PREVENT hearing loss because his ears don't drain on their own, and as AllisonF said below, the hearing loss is a result of the fluid in the ears, not the tubes. I wouldn't worry at all. The procedure is extremely short if they are not having anything else done, so they are not under anesthesia very long at all.
My son has rarely had ear infections (which is highly unusual for a child w/ a cleft palate with fluid-filled ears! They usually have infections all the time--we were just lucky) but people I know whose kids got tubes for that reason said that they made a world of difference.
He does have to wear ear plugs when he's in water because he has tubes, so that is a slight inconvenience, but not a huge deal. One Step Ahead makes an Ear Bandit and some great ear plugs, and using that system he even took swimming lessons last year. (And their plugs were so good, I stopped using the Ear Bandit, which is supposed to hold them in while you swim). I've heard so many people say that their kids didn't take swimming lessons b/c they had tubes, and there's no reason to avoid them because there are some great and inexpensive ways to keep water out of ears.
If tubes can help with your child's ear infections, I see no reason to avoid them. We have no problems.