In short, no. I usually try to stay within the same shade, if that makes sense. Darker slacks with darker tones in the jacket.
The navy blazer with tan slacks is the exception and though I'm not fond of tan slacks, it is a standard.
I would definitely not do gray on gray, regardless of the shade differences.
I am of the opposite, where I prefer greater contrast between jacket and trousers, usually with a darker jacket and lighter trousers (I have done the opposite with lighter colored jackets in the summer).
For example I like a navy or dark blue jacket with tan, tobacco brown, light grey, mid grey, and off white. I might even do a light blue. If I had dusty colored trousers (in say nantucket red, or faded green) I might wear those as well.
A navy jacket and charcoal trousers is a combo that I certainly see often enough, but I do not care for. I am of the mind that even from a distance there should be an obvious difference between jacket and trousers. Charcoal also doesn't look great with jackets in shades of brown, in my opinion (although I've seen examples that are touted as being good). A good article on charcoal trousers
here.
Outside of contrast, I basically look at browns and grey as neutrals that work with any other color (but not necessarily with each other, outside of darker brown with light grey, which I do like). Navy works with pretty well everything as long as there is enough contrast to differentiate.
