He's been doing that the whole time actually. He was on Bluebloods before he was on Arrow. So that shouldn't have had anything to do with it. I think he's only been on Bluebloods once this season so far. But the point is, it is possible to do two shows at once. If they are staggered, then it would be even easier.
If anything, I think Sasha is a goner. Being prego on a TV show that kills characters off every few episodes isn't a good way to have your character stay alive And I don't think they'll be able to pull the "Bob got her pregnant" card because I imagine she'd have noticed something before really starting to show, which she is by this point. You never really saw Sasha from below chest level all through the least episode. They can't keep that up much longer without it looking noticeable. So I would expect something significant to happen to Sasha rather soon.
Though I don't think she'll be around too long, her pregnancy has good timing. I don't think it will even be shown. Aren't they done with filming this season? She'll have it by the time they start filming the next.