Will this PSU work for my GTS 250?


You don't know that. The label says "Maximum power". We have no way of knowing what the total 12 volt power is. And because they are not telling, it's probably pretty bad.

The Apex is junk. Note the voltage selector switch. That means that it is an obsolete design without automatic PFC. Efficiency is probably around 70% instead of the 80% + that more modern PSU's have.

I'd recommend something like a
Corsair 450VX (33 amp 12 volt rail)
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139003

or an Antec 500 watt BASIQ
http://www.newegg.com/Product/Product.aspx?Item=N82E16817371004
http://www.hardwaresecrets.com/article/792
 
That is not a recommended PSU but if you have it it will work. It is not as simple as adding the two rails together usually total wattage for the +12volt is stated under neath the sticker I would be surprised if it is more than 360 watt (30amp) on yours.
If you do not already have the PSU this 400watt Corsair is a high quality unit and will run your card no problem http://www.newegg.com/Product/Product.aspx?Item=N82E16817139008