Unfortunatlly no. I wish I could tag local as well, but you have to at present tag what has been uploaded to the web.
Picasa Web Albums does face recognition
With Picasa 3 out of the way, we gave some of Picasa Web Album's new features a run-through to find that they compliment its desktop brethren's experience pretty well, if not awkwardly at times. Easily the most impressive new feature is "Name Tags," which harnesses facial recognition technology to automatically identify people in photos. This makes it easy to, say, keep a running album automatically updated with photos of Cousin Erin or your parents, but this all has to be done on Picasa Web Albums. Picasa 3 does none of this work on the desktop, and doesn't appear to gain any of the advantages of all this automation and facial recognition tagging.
Link to full article
The new Picasa 3.5 contains a facial recognition feature similar to the one already present on Picasa Web Albums, but letting it run over your likely vast collection of assorted photos stashed on your hard drive is a lot more convenient. Picasa creates a new sidebar menu list of "People," and asks you to name the folks it finds in its main "Scanning" menu. If you're signed into Web Albums with a Google account stuffed with contacts, that's pretty easy, actually—just start typing a name, then select the contact that pops up as you type.
Today, I'm happy to announce that we're releasing Picasa 3.5, a new version of our free photo editing software. This version gives you the ability to add name tags to your photos, using the same facial recognition technology that powers name tags on Picasa Web Albums.
Official Google Blog