Spanning tree + Allows vlan question

Probably an obvious question...but with regards to spanning tree...

I have 2 access switches connected to the core (root). Each access switch is mostly dedicated to a particular VLAN, lets say VLAN100 and VLAN200 respectively and are limited to these vlans thru "allowed vlan" on the trunk.

Now I want to add a redundant link between the 2 access switches.

So now lets say the link to the core goes down for the switch with VLAN200 ports. Those ports now have to traverse the redundant link and ultimately thru the core link that is only allowing VLAN100. This effectively blocks VLAN200, am I right? So for this to work I would need to add all possible VLANS that might flow thru those trunks to the core?