Can you put the armoring from the PVP sets into the shells of the PVE armor and get both bonuses?
NO. You will have only one bonus.
WH (61 level) PvP Armor mods will override the gearset bonus.
With any other armor mods the set will retain gearset bonus.
That is nice for PvE. You can have Rakata/Columi gear piece, insert there the Campaign, BH mods and have the Rakata set bonus.
For PvP, if you want to use PvE set bonus and not sacrifice the Expertise, you should use only BM armor mods that have slightly lower stats than WH ones and what more important - have less Armor Rating.