It really depends on who stays and who goes. Big organizations are collections of individual teams. Each key part of the site has a team behind it with 5 - 10 engineers.

If the departures are such that for each team, 1 competent senior engineer remains who can keep that domain running, then Twitter could be unaffected with 1/5 of its workforce. They might not be building new features, but the current site could function, which is reasonable since the current site is arguably feature complete.

But in reality it won't be as clean as that. If the whole localization team quits, suddenly the site won't be translated to other languages. If the whole mobile release team quits, suddenly the Twitter app might disappear from the app store. Or the security team is gutted and suddenly everyone's passwords are leaked.