Routing over prvt vlans

I don't have the kit to mock this up at the moment, so I thought I would ask if this makes sense.

The issues is I want to run both Local VLANS and site wide vlans from my access/distribution switches. So the issue is how to keep the number of vlans down, the redundancy up, and have as few blocked links as possible over the routed paths. while still using RSTP for site wide Vlans..

(I wish you could up load better pictures, they always seem to lose quality when I try! )

Any way the basic idea is that Distribution switches have a vlan interface in an isolated prvt vlan. and the core switch has a vlan interface in the primary vlan.

Am I correct that if all the switches are running a routing protocol, that the next hop to get from a network connected to one distribution switch to a network connected to another. would be the IP of the core switch?

There is much more to the network than this, but I am scribbling ideas down on paper at the moment, and I just want to know if this would work, as it would make the design much simpler.

Cheers