That is a tough question. In your case, I want to say yes, but I just don't know. I literally have zero experience doing the splitboard thing on the east coast.
I will say that the ski crampons are probably something you'll need infrequently. Even in Washington, where things are more mountaineering like I've broken out my crampons twice in three trips. Maybe try to pick the brains of some of the locals if you find some?
I think at some point you'll want to get them, but maybe not right away.