Yes and maybe. Dogs do not "generalize" like humans do so let’s look at things from a human perspective.
You’ve just landed a new job and part of that job is to learn new software. Since you have never used this software, they give you a technical manual to read over the weekend. You can read it while sitting in a chair in your living room, outside under your favorite shade tree, or while sitting in a busy airport.
No matter where we are you still know how to read and comprehend the words.
A dog's brain works differently than ours. They take in all enviormental destractions (new smells, new people, new everything) much more than humans do, so it's almost like learning the behavior all over again. But the good news is, if they've been successful with the behavior in the past, they quickly re-learn the behavior in their new environment.
This is a diagram where your dogs microchip was implanted. As time goes on, the chip can move down their back or legs, so it is very important when scanning a dog for a chip, you scan the entire body.
Your dog may have one of several brands of micro chips.