Can this be done?
I have several covers defined for record A with cover types defined as well. I would like to copy all of those from A and paste them to B(and possibly others as well)
Yes, it can be done, but only one by one.
Right click on the "source" cover for Record A in the (left) tag panel and choose "Copy cover".

Then select all the target tracks B and right click again in the Cover part of the tag panel and choose "Paste cover".
If you want to remove existing covers for B you can do that first, again with a right click and "Remove cover".
If you have - as an example - 1 x Front Cover, 1 x Back Cover and 1 x Booklet, then you have to repeat this copy & paste 3 x. Once for every picture.
I was hoping to grab them all as a group and copy/paste them. If this is what I need to do, I will do this, though!