According to the answer I found here :
https://community.cisco.com/t5/switching/communication-between-the-secondary-community-vlans-hosts/td-p/2648508
... this seems possible based on the design I have given.
[Community Vlans] communication over the promisc port would be allowed only if the device connected to that promisc port was willing to do hairpin routing - that is, receive and forward a packet back the same interface. Usually, you do not want your different community VLANs to communicate to each other - that is why you created them in the first place - so you'd usually make sure that whatever device is connected to a promisc port, it does not do routing or is prevented from hairpin routing via an ACL, for example.
I have also asked a CCIE colleague which just confirmed to me that communication between these two vlans would work.