Grease won't soak inside the rollers much though and that's where the lubrication is needed. I try to get 1500-2000mi out of a mountain bike chain and at least 4000mi out of a road bike chain. That is only possible with a strict lube schedule and the correct lube.
Mine is clear and with wax in it. Provided the chain is cleaned well enough before each application you can almost see the links slurp up the very runny lube. It's almost like water.
The problem is no matter what color the lube has the road and trail grit gets mashed into it. On singletrack my chain always turns brown or gray-brown, depending on how much crushed decomposed granite there is. On bike paths the chain stays nicely clear. On roads with lots of vehicle traffic it turns black quickly and then I always wonder what gets into my lungs. Probably from all the Diesel engines.