As the title says, what happens if I develop a color film exactly as I would do with a black and white film?
You can develop E6 and C41 slide or negative film with B&W developers and get monochromatic results. With Kodak film you'll have the orange cast, but you can still scan or print from the negative.
I've seen mention of people using Acufine/Diafine and Rodinal, but never tried it myself. Good examples here: Cross-processing colour film in b&w chemicals
You can also use C41 processing on B&W film if you skip the bleach step, which would wipe out anything on the negative.
E-6 will give less than optimal results developed in B&W, you'll lose a lot of contrast + there will (probably) be a dark brown hue to the negative. C-41 in B&W will give better results than E-6, but will still be inferior to developing in C-41. There will be an accentuation of the film grain, especially if what you're developing is low speed. I've played around with E-6 and C-41 in D-76 1+1 and have been pretty pleased with how C-41 comes out, slightly less pleased with E-6 due to the dark brown hue. Caffenol will also work as a cheap developer for E-6 or C-41.
If you're just starting to experiment I'd start with some cheap Kodak Gold or Max 400 and shoot things you're not afraid to lose (i.e. No family heirlooms, No shots of the Loch Ness Monster, No Bigfoot sightings. You will inevitably mess up and totally ruin a roll or two, but don't let that discourage you, experimental photography is tremendous fun.
Let me note that under no circumstances should B&W be developed in an unmodified C-41 process. The blix, or if you're using a bleach separate from your fix will completely wipe a B&W negative. The bleach doesn't play nice with a B&W negative, so if you're going in the opposite direction, just leave the bleach out of the process. If you're using blix... Well, don't process B&W.