Will my psu handle this?

I don't think the Real Power Pro 850W is the worst PSU in the world, but it is quite old and there are better PSUs around today. The Corsair 850TXV2 is one example.

Review for CM Real Power Pro 850W:
http://www.hardwaresecrets.com/article/Cooler-Master-Real-Power-Pro-850-W-Power-Supply-Review/538
Review for Corsair 850TXV2:
http://www.hardwaresecrets.com/article/Corsair-TX850-V2-Power-Supply-Review/1298

This uses the same internal design as the Corsair unit, but is usually cheaper:
XFX Pro 850W Core Edition 80Plus Bronze $120 ($30 rebate, $6 shipping)
http://www.newegg.com/Product/Product.aspx?Item=N82E16817207011

I assume that you are going with an 850W unit because you want the option to add a second card in the future.