They can't insert it the same day, as it needs to be ordered and you need to have your consultation first. I also had to get a blood pregnancy test done. My OB prescribed Mirena at my 6 week PP visit, and it was then inserted 4 weeks later.
If its covered under medical insurance, it can be done same day. It only has to be ordered if its covered under pharmaceutical. However, it may take some time for them to figure out which one its covered under, and then it wouldn't be same day. So...yeah. Definitely call ahead.
FWIW, my OB recommended I wait until I'm actually on my period to get it because its supposed to hurt less.