I'm on the fence on getting the Titanfall expansions, but if I do so, will I be able to play with friends who don't have it?
You will! The Expedition map pack has its own lobby, however, the maps are also in the standard Attrition and Hardpoint playlists.
That said, the new maps will only come up if everyone in the lobby has the DLC. So you'll be able to play with non-DLC friends, regardless of your owning said DLC.