Mid 2010 Mac Pro with no video card; will it run with new HDDs?
I have 2 mid 2010 MacPros and have been able to run both without a GPU. If you can load OSX with screensharing turned on onto a drive using another Mac in Target Disk mode you should be able to plug that drive in and boot it up.

I have this running as a media and file server and it works great. Also cuts back on the heat as I loaded my pro up with 6 HDDs (4 in the trays and 2 using the OWC 3.5 adaptor in the CD Drive space). Set up an SSD via a PCIe adaptor for OSx. It works perfectly.