Yes, I believe it should. Make sure you check the fuse, and try a different one even if it looks ok.
Another way to test is to disconnect the temp sensor that turns it on (plugged into passenger side of radiator) and then play with the 3 holes it has. When you connect 2 of them, it should turn on. I don't think you can harm anything by trying all combinations, there's 2 positives (2 speeds) and 1 ground/negative. You short circuit the switch basically, not the radiator itself.
1998 BMW 328is - summer
1994 BMW 325i - daily
1992 BMW 325i - gone
1988 Mercedes Benz 190E 2.3-8V - sold