Yes of course. Bigger card is always better.
Edit forgot to answer the question: Personally I don’t reach the written TDPs with my system. R7 1800x and 2 RTX 2070s. I can’t speak for the 1080 but I don’t think they really reach the max. Vendors tend to give themselves some leeway.
Anyways, you also have other components that need power. So all in all the next step should be a new PSU. Just keep an eye on it.
At a minimum you need to make sure your PSU has the appropriate type and number of power connectors to support the cards you want to put in it, since the more power hungry cards require more/different power hookups than the lower power ones.
600W might be risky for two 1080 class cards, and so a PSU upgrade might be a good first step.
Öhm, But he has a 850 Watts PSU.
@daddario90
Any way. Throw your parts at this:
It will give you a really good estimation of what you need.
Oh, misread then. I’d think that would likely be OK, but check all the numbers and cables.