As someone who's written replacement backend Xbox Live server infra, I can confirm that system link is very nearly the same base protocol set as is used by Live. They must have had that nailed down pretty close to launch, and were mainly working on support services that live needs but system link doesn't up until Live actually launched.

They were probably already working on it

The game was actually close to ship without multiplayer, it was an afterthought. Some devs have talked about this (iirc, Marty O’Donnell was one of them).

The game being an FPS was an afterthought, too. Originally, they were working on an RTS.

I wouldn't call it an afterthought per se, more a pivot with a lot of work. It was already an FPS when it was shown off at MacWorld'99.

I’ve heard this was also the case for Goldeneye on the N64

Goldeneye is one of the best case studies for why companies should give their engineers room to experiment. If I remember correctly, the multiplayer mode was originally a side project of one of the engineers and was added near the end of development.

This isn't to say the campaign mode isn't good, but the ability for boys to play a shooter game against each other on the same console is what made that game.