An SSD would physically work with that hardware, but from what I can tell the OS that comes with the Precision 670 is XP (which isn't an ideal partner for an SSD) and I can't see which version of SATA it supports. However you may not be able to clone your SATA > SSD to get a smooth handover - I'm sure someone here may have tried it and will be able to advise .
Do you have your full system specs and we can take a look at it .