Is it possible to print using pantone 877u on uncoated stock and varnish the area, in a way to achieve the effect of pantone 877c?
The letter at the end of the pantone number U and C are just artificial rendering of the metallic ink on coated and uncoated paper for your display.
Your printer will use the same can of pantone 877 ink no matter the 877U or 877C you chose for your design!
So if you want to know and see how the final result will look like once printed, you should look at an official pantone color book or ask your printer to show you examples of printed projects using that metallic ink on the type of paper (coated or uncoated) you plan to use, with varnish or not.
Note that the varnish will not affect much the color of the metallic ink if it's applied on top of it. What makes the coated and uncoated ink color vary is how the ink "sinks" in the paper.
You can still print the metallic on top of a varnished zone, on an uncoated paper. It creates an original effect, a bit like a spot varnish would. If it's a thick UV varnish, the metallic should be closer to the effect created on a coated paper but the ink might look matte.
This can work because metallic inks are more opaque than the other colored inks in offset printing.
Might be simpler and nicer to use a coated paper, and a spot varnish that is matte, if the budget allows it, and it's the effect you're looking for.