I have a 10-gallon tank with two goldfish and no plants, just gravel. Is it OK to add one live plant? Does the plant help with filtration?

Sorry to tell you but no, you don't have enough room.
Fancy goldfiesh require 10 gallons each and commons need 20. Plants to help with filtration by removing nitrates, but a plant won't be enough to control the waste.

You can add a plant, that would be fine, but it wont be enough to help with filtration, it will just be a pretty snack you do need to upgrade though as your fishies will outgrow your tank soon!

Sure, you can add the plant but don't count on it to be anything more than beauty and a possible snack for your fish. Plants do create oxygen by converting the nitrates, but one plant isn't enough to do that and you don't have enough room to add the amount of plants necessary to do that.