Well, the private AS # will not be propagated between the different ISPs. As BGPs loop detection algorithm is to watch for its own AS# in announcements, you run the risk of looping, using transit to try route between your border routers (remember, eBGP has admin distance of 20, iBGP has admin of 200), etc. This is not a good thing! (you could mitigate much of this with carefully applied route-maps that block receiving your own prefixes).
People receiving your announcements will also see inconsitent source ASs for your announcments and so you run the risk of some people not installing them.
Warren.