Yes! That power supply should be more than enough to run your GPU as it uses up to 200-230 watts while gaming. Also, good choice on the PSU as it is power sufficient and leaves room for future upgrading!
Hey will my psu Thermaltake 600W 80 Plus White Smart Series - PS-SPD-0600NPCWBZ-W run a Sapphire Nitro+ RX580 8GB 11265-01-20G without any problem ?
Well, how old is it?
It only puts out 42A on the 12V rail.... That makes it about a ~ 500w PSU really. That's if it can actually put out 500W, that model really isn't a very good quality unit.
I would recommend replacing it with a higher quality unit before using that new RX 580.