Also, does the card suck more juice while it is rendering detailed graphics - like if I were to run StarCraft 2 under ultra mode?
Yes it does. It will hit peak demand running the detailed 3D graphics.
SC2 would be a good test to see if the PSU will hold up. It will be easy to tell if the PSU isn't up to the task.
First sign might be the PSU working extra hard - loud fan and blowing hot air out the PSU fan. And if it can't hack the power demand you'll see shut downs, or game freezes.