That is true, but only if we are the only ones using private ASNs.
But if happens that some people already uses private ASN for other purpose, they would be in trouble connecting to 44net... because there would be collisions.
I see no point of using public IP addresses and route them using private ASNs. It may be that I do not understand BGP well.
It is important to note that the routing in this overlay network, let's call it BGP44 from now, is running as a separate BGP instance that is not combined with BGP announcement to internet or private use of BGP. The BGP44 instance will only distribuite the routing info for AMPRnet subnets, similar to what is now in the IPIP routing table.
Also, even though there could theoretically be collisions, in practice there is not much risk because there are 94,967,295 available AS numbers in the space that we use. That is 8 times more than the number of IP addresses we have left.
Rob