Should I power the merchant room?
Aslum's answer is incorrect. Powering the Merchant room doesn't generate Dust. It only helps you to build defenses to protect the Merchant.
Regarding Dust generation, after you have researched the Shop (Major Module), build one, at which point the Merchant will be teleported to the Shop. Afterwards, if you select a hero to Operate the Shop, you will gain Dust per turn.
Source
When I have no resources to build a shop, I am powering the Merchant room to prevent enemies from spawning there and killing the merchant.