We are homeschoolers, from day one, long before my dd ever stepped into a gym. We chose to homeschool for many reasons that had nothing to do with gym but now that she's competing, we're really glad that we have done it.
In order to be eligible to receive a scholarship of any sort, you need to be able to get into the school for which the scholarship is for. And the vast majority of colleges accept homeschoolers. Many colleges have a separate track/admissions process for homeschoolers. Homeschoolers have gotten into just about any school traditional schoolers have, including Ivy League schools. Just read up on the particular college and see what they require of homeschoolers.
I admit I'm a bit irked by the implication that homeschoolers aren't "normal" or don't have "normal lives". Of course they do. My dd has friends from her gym, dance and tennis classes. She also plays with neighborhood kids, as well as her siblings and family members and friends from church. No one can tell she's homeschooled because she acts like everyone else. She's normal and has a normal life!
Anyway--at age 9, she's reading at 10th grade level (this was determined by testing), and is almost done with 4th grade math. She'd just be starting 4th grade now if she were in traditional school--so homeschooling has clearly not impeded her academically.
Research your options, and especially your homeschooling options, if you choose to homeschool. There are literally thousands of homeschooling programs out there, and the best thing is, you can customize it to work for you. We finish all of our schooling in 3-4 hours, no homework. We take vacations whenever we want. It's great.
It'd totally work for you, if your goal is to turn elite and spend more time at the gym. You can finish your work in a shorter amount of time, even if you use an academically rigorous homeschool program, and take time off to go to meets when you need to. You'd have plenty of time to hang with your friends, probably more than you do now.
There is no reason to assume your life won't be normal or that you won't have any friends. Please.