For instance: is it possible to get the Dunwich expansion and play with all the extra investigators, items, encounters, and so on that add to the basic game, but without using the additional gameboard and the new concepts, or will this just make the game broken?
Depending on what you cut there might be some rough edges. Like you will get a train pass at the train station which has no function without the extra board. However, if you are willing to accept/fix these minor problems with a spontaneous house rule (ignore, redraw,....) it should work fine. No balance issues.