SpanishDict gives lots of excamples. I did not specifically see to cover as in cover a check http://www.spanishdict.com/translate/cover
The SpanishEict gives this example: 9. (to commentate on) a. cubrir He covered the war in Afghanistan for the New York Times.Cubrió la guerra en Afganistán para el New York Times.
Babella from Spain native speaker says above:
"I do not know if in some places that is what it means, but the first thing that comes to my mind when I read "lo voy a cubrir" es that you will cover something (or someone) with a blanket or something of the like."
So far that is the only native speaker that I see.
No, the use of "meet" that "cubrir" is synonym of is the one that means you have reached a quota: I have met the sales quota = He cubierto el cupo de ventas.
A little tip: most of the times stay with the first or two first options, the rest are usually quite specific and you will not be using them that much; you can get to them later ;]