Are you looking to use the Groove because of its price or its portability? Such as do you have a better dedicated system at home, and are only looking to use the Groove for travel or at work?
The short answer is yes, the Groove will drive the HD800 - but so will an iPhone if you are willing to compromise. My question to you - what compromises are you willing or trying to make by driving the HD800 with the Groove? Is there a budget? Do you already have the HD800, or are you thinking about purchase of a top headphone in balance with the purchase of an AMP/DAC? If you have not purchased the HD800, there are reported to be a few newer headphones, which are more balanced sounding, out of the box, and would be easier to drive via almost any source.
Or have you already purchased the HD800, and are now trying to address its limitations - treble peak and low bass output? There are not too expensive fixes for the treble issues, which you could search for that could make the HD800 more balanced and finding an AMP/DAC simpler.