Assuming your links from the access-layer to the core switches are layer 2 links then yes it would work without a connection between the core switches. HSRP traffic would go over the access-layer links which might or might not be what you want.
Where there would be an issue would be you could end up with suboptimal paths.
eg. Switch C's path to Switch A is forwarding and a client on switch C in vlan 10 wants to talk to a client on switch D in vlan 50.
Traffic goes from switch C to A (HSRP active for vlan 10) is routed onto vlan 50 and down to switch D.
If switch C to A link goes down then switch C now sends traffic to switch B but your'e active gateway is still on switch A. So B sends traffic to D which is then sent to A. Then traffic is routed onto vlan 50 and sent back from A to D.
If you had a link between A & B switch C would send traffic to B which would send it to A which would then send it to D.
Of course the con is that if you connect your core switches together you now have created layer 2 loops in your networks and spanning-tree now has to step in and block some of your links.
Thanks for the nice explanation. So as per your description, link between core switches is only required to have a direct path between the core and to have optimal flow of traffic. If required then it may be avoided (but not recommended)
Hope I have correctly understood your explanation...
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