Greetings!
It should be able to. The GT 710 pulls it's power straight from the PCIe slot, and works very well for this application...plus it is a small form factor card and looks like it should fit without any issue. You may need to ensure that you can swap on the smaller sized bracket that will fit your case, for a standard bracket is going to be too long. Most GT 710s come with this option, but some may not, so just double check if you haven't purchased it yet.
Here is a link to a fellow installing an AMD GPU (A very similar sized card) into his HP 8000 SFF:
https://www.youtube.com/watch?v=A7m2H0_KOF0
Hope this helps!