In reply to Sam Beaton:
Short answer... Yes.
Long answer... It might just work straight away by logging in with an Epic account that they already have (Epic being the makers of the game). If they normally play exclusively on Xbox, they might have to jump through the extra hoop of creating an account with Epic and adding their friends to that account. If they're already playing on more than one platform (e.g. sometimes playing on Xbox and sometimes on mobile or PC) then the transition to Switch should be seamless.
I would add that, for kids of the age that are normally heavily into Fortnite, platform loyalty can sometimes be a big thing. It might be worth finding a way to talk to them about it before committing money. If they normally play on Xbox, they might think the added portability of Switch is awesome or it might be like buying double-stemmed cams for a committed single-stem zealot.