Yes it should be fine, (I presume you are talking about the sg07)
600w psu is more than enough for 1 graphics card.
Enough room for graphics cards up to 310mm and the longest 7870 I could find (HIS HD 7870 ICEQ) is 285mm.
600w is plenty for a single gpu.
So do you have the 7970 or 7870? The 7870 has two 6 pins and the 7970 has one 6 and one 8 pin. Does the psu only have 2x6 pin connectors?
If that is the case you will have two pins unpopulated and the card will not work. You will have to get a 6 to 8 pin adapter or one may of shipped with the card and I believe that will work.
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