Just to clarify....
Most of these DSL/cable routers use the same base chip sets/technology.
Most DSL connections here in the UK operate at about 600 kbps download, the local ethernet port of these units is usually 10/100 mbps, ive seen a very low end cheap D link router route/NAT an internet connection at over 5 mbps without issue.
So the answer to your question is no.... unless you have a real peice of shit router the slow down will be caused by your lack of internet bandwidth.