yes, it will depend heavily on what the rest of the system is... ie, mobo, cpu, other add in cards, number of optical drives, fans, hard drives etc. it will also heavily depend on the make/model of the psu.
A high quality psu should be able to handle it, but if it is cheap then I'd doubt it. Also, the number of amps on the 12v rail will determine a lot as well.
For example my bro has this rig:
Celeron D 2.66Ghz
2x512 Corsair PC3200C2PT
1 DVD drive
5x LED case fans
now, you might be thinking no problem... just as I did, until he sent me his rig to fix it... then i took a closer look at his psu. it's a no name brand 420w w/ only 18a on the 12v rail. most of it's power is in the 3.3v and 5v rails. Also, his psu is only native 20pin ATX and his mobo is 24pin. So when all that is taken into consideration I highly reccomended to him that he purchase a new psu.
I hope this explains well enough that to fully answer your question we need more information. However, even with more information all we can give you for an answer is 1) that most-likely will not work 2) you definately need a new psu or 3) that should work.
I would say you should get a new psu... but you may be alright w/ what you have.
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