Yes, UK nationals will go through the same procedure. Not a big deal because their country is part of the Visa Waiver Program. The aircraft will arrive as a "domestic" in EWR.

In other words, pre-clearance is just that - once you've gone through it in DUB, you can pretend that you're "in the US" already. (Of course you're not 100%... but I&C related you are.)