Automatically share new photos with photo stream?
No - I'd suggest dropbox as an alternative. It's still not flawless since you need to open the app to start pushing new pictures after taking them.

Here is some discussion surrounding the dropbox implementation:


Two Photo Streams, one iPhoto library
Can photos taken with my iPhone (and Apple ID) stream to my husband&#39;s iPad (and Apple ID)?


Alternatively, you could use a specialized app that includes automatic upload, for those are dime a dozen.