Nope. How big of a psu do you plan to get?

Even if you get a high wattage power supply, it only matters what is pulling power from the power supply. But yes you should be fine unless you have other high wattage appliances on the same circuit

You shouldn't need a dedicated outlet but I would change it out if its old. If it can't the prongs well anymore then it's worth switching out. Just make sure to cut the power and use an outlet checker just to be 100% sure it has no power. A lot of times a fuse box will be miss labled so never trust it to be more of a starting point. I personally changed all my outlets when I bought my house over a few days. I felt it worth it.

Check the wiring itself for a ground lead - if none, then rewire is the only viable option and you MIGHT also have to replace the fusebox/breaker panel.
At least you'll have the old wire to "pull" the new wire with.
 

If your outlets lack a ground at all I would consider looking into the cost of adding one. Some appliances in your home should really have a ground like the kitchen and bathrooms. They should also have GFCI outlets within six feet of any source of water.

QuintLeo
If you only have 2 conductors at the outlet, both insulated, there is NO GROUND and tying the ground on the outlet to ANYTHING does absolutely nothing.
Tying the ground on an outlet to stuff like a water pipe, conduit, etc is NOT A RELIABLE GROUND and likely is also not a ground at all.
 
Bdary's advice is A VERY BAD IDEA as well as being a violation of the NEC.
 
 

My advice is a good alternative to running new wiring to/from the panel which is quite costly.  However, a little more detail is needed in what I said in my post above.  Here are some examples of what I was describing above with more clarification.
 
https://www.wikihow.com/Ground-an-Outlet
https://www.thisoldhouse.com/ideas/replacing-two-prong-receptacles
https://structuretech1.com/how-to-fix-ungrounded-three-prong-outlets/
http://mbi-us.com/3-choices-replace-nongrounded-2-prong-receptacles/
 
As you can see, rewiring is NOT "the only viable option".

AS I SAID, and is even mentioned on one of those sites you cite, counting on a pipe or other such "grounding" methods is a violation of the NEC.
NOT SAFE.
 
The only allowable grounding method under the NEC is a continuous ground lead (NOT spliced) that goes back to the panel.
 
I've seen a LOT of installations that violated code - and seen a LOT OF ISSUES caused by those installations.
The code is written the way it is for many reasons, all involving safety.
The entire REASON the code exists IS SAFETY.
 

Make sure if you do change an outlet that the black wire goes to the brass screw and the white wire goes to the silver screw and the ground (green or bare) goes to the green screw.
If it is BX wire, that is wire with a metal jacket, that metal jacket is grounded at the panel.
In offices we used to run isolated ground receptacles, they are the orange ones you see in a business office. It helps stop the natural to ground voltage issue if there is one.
Try not to plug anything else in the socket with the computer like a big fan, vacuum cleaner, hair drier ect.......  
If you are using a big watt PSU make sure the wire from the wall to the PSU is 16 or better yet 14 gauge wire 14GA.  It says it right on every power cord. 
Do NOT use the wire from the 650W PSU on a 850 Watt or larger PSU. 
I was lazy and did not change the cord, it got very hot to the touch. The system had random reboot issues, took a while to fine the problem.
Found it by luck reaching behind the comp. and just happened to feel the cord and it was hot!
 
Please be careful.