A full scholarship is strong documentation to get a deferment, but the trick is not to leave it for the last minute. Go to the military board with the scholarship grant letter and proof of enrollment already in hand - the sooner you do this before September, the better, because some boards have pretty slow procedures.
During college you can renew the deferment, but there's a detail that sometimes gets overlooked: not all boards accept automatic renewal just with proof of enrollment. Some require you to show up in person to confirm you're still enrolled, others want updated documentation. Best thing is to ask your board directly what their protocol is for renewals and keep a mental calendar of it - like, go a week before each deadline expires so they don't catch you off guard and you have to stop everything.
After you graduate, then yes you have to do the service, unless you have other situations that allow exemption, which is less common. But as long as you're in university and keep your paperwork in order, it's not stressful.