This is not what you ask, but may be relevant to what you want to do.
Reviews of pico projectors have not been favorable for their image quality, tend to be low quality with color/saturation/sharpness/details problems. You can easily google the reviews and read them yourself.
Tethered shooting has been done for quite a while, mainly among the pros or serious enthusiasts. This is mainly for Canon and Nikon cameras. You can connect via USB from camera to computer, and record/display photos or even video directly without wasting time with the memory card. Tethered shooting is mainly for photos, most commonly done in studio and on-location pros to show clients images immediately on the computer or laptop. But I have read that you can do tethered shoot for D-SLR video too. Viewing photos on computer or laptop screen will look much better than the pico projector. You can google tethered shooting easily and read it yourself.
I am trying to find a pico projector I can hook up directly to my camera so I can shoot photo's/video and then immediately display them. Has anyone done this yet? It looks like a couple of them come with video inputs like the P2 from Aaxa tech and the Optoma Pk101. I like the Optoma because it is a lot cheaper but the P2 is a lot brighter. How important is brightness in a projector? It's not really that big a deal is it?
Here is the P2: http://www.aaxatech.com/products/p2_pico_projector.htm
and here is the Pk101: http://www.tigerdirect.com/applications/searchtools/item-details.asp?EdpNo=4695510&SRCCODE=WEBGOOSKU25&cm_mmc_o=mH4CjC7BBTkwCjCECjCE