You'll probably have routing issues.
I know I experienced something like this with my brother. His Linksys worked perfectly until he tried to VPN into work and they use the same 192.168.1.x address space. I ended up re-configuring his Linksys so that locally @ home he'd be 192.168.3.x and then thing were happy when he VPN'd to work.
The problem is your local device has no way to know if (for example) 192.168.1.10 is local or VPN if both networks use the same RFC1918 address space.