Andromeda has a different main character, different galaxy and probably takes place a long time after the events of ME 1-3. That's a "most likely, yes".

Considering there are some alien races that live for a thousand years and some that aren't even biological life forms, I'm sure you'll run into some characters introduced in 1-3, but they'll probably be re-introduced for new players. And yes I do want to continue my relationship with Liara.