If I set up a tunnel from site-A, and another tunnel from site-B, can unique addresses be routed through this tunnel?
I'm not completely understanding...are you saying there is a private (like VPN or Ethernet handoff) connection between the two?
If you mean setting up your own tunnel between devices and not using HE, yes.
Or you could use something like OpenVPN over the HE tunnel, which will encap that traffic in that VPN.
But no, ULA will not cross an HE tunnel, it isn't routable.