yes...

1. The fan should flicker on start-up
2. The fan should come on with AC..if AC is working
3. I am told if you unplug coolant temp sensor on lower Radiator hose it will come on when you turn the key ...I haven't tried it.

If the fan fails to turn on in above tests, replace it.

you can also activate it with INPA and other good quality 2-way scan tools.
and of course you can lay any known-good fan from an E46, E39, E83, E53 E36/7
on top of your engine, plug it in to your fan's connection and see if it works.

I like the TYC brand fan for E53 found on Amazon.