I'm just assuming they'd drive the point home as much as possible, otherwise there's really no point to it. If she just interacts with the Doctor normally, then what difference does it make what time period she's from?
You can take any good idea and ruin it like that, so it's no reason to diss a particular bad idea.
Food is good, right? Everyone likes food. But it would get old real fast if we tied people to chairs and force fed them until bacon came out of their noses and they died. I'm just assuming that's what would happen if we tried to cure world hunger. There are no other possibilities.
Having a modern day companion gets old, as well, and we already have
done that to death. No reason not to try something new for a while. It's not like you're locked into a contract for the rest of time. Eventually, the actress is going to get offered a movie or Moffat's going to go off and remake Dracula or something and I'm sure we'll be right back to having the Doctor meet a new young, British female companion from the modern day ONLY THIS TIME SHE'S FEISTY AND A REAL EQUAL TO THE DOCTOR UNLIKE ALL THE OTHER TIMES SO IT'S TOTALLY DIFFERENT!
Having said that, Clara is hot, so whatever.