Impassable borders stop resources?

[Targa]

Just a quick question for verification of what I just saw. This time I chose to try the fortress with 50 admin, and as usual, I conquer all adjacent provinces to draw in their resources. However, there are two adjacent provinces that are blocked off by a mountain range (so although they touch my home province, I have to take my troops through a couple of other provinces to get there). It makes sense that the impassable mountains also stop resources from coming in. I was wondering this, and checked my resources in my home province before and after conquering the "mountain province", and they stayed the same. Has anyone else seen this behavior? Just checking to be positive that it's a waste of time trying to get resources from a province that's blocked off by mountains.