I'm pretty sure Alec being turned into a vampire would stop him from being a Shadowhunter, which would be a bit of an issue. That and the whole not being able to go outside during the daytime thing (although magical boyfriend who can portal them anywhere would circumvent that problem).

I mean they could literally make up something to make him immortal if they wanted since it's a fantasy TV show, but I'm expecting this to go down more like the books where they both learn to live with it and cherish all the time they have before Alec dies.

(I mean personally I'd rather have Alec be immortal or Magnus loose his(willingly though, and not have Alec try to take it away like he does in the books), but I'm not holding out hope for either of those options).