I hope not - this is not an interstellar soap opera
I hope there will be a brand new character, new adventures, etc. But I hope, if there will be ME4, it will check your ME3 saves like Dragon Age 2. Not every decision but the main picture about the galaxy Shepard left behind.
And I also think we will meet major characters again in cameo roles, you will meet Shepard's ex-squadmates. For example:
Liara - she is young, she can live a thousand years, and she is the Shadow Broker now
Wrex - he is not so young but I think he can live a few more centuries

Tali - an old Tali could be an admiral or politian of the quarian people
Garrus - he could be a very experienced and feared spectre at this time, or a general of the turian fleet
Or you should meet not squadmate characters also, for example:
The Illusive Man - humans can live longer at this time and I think TIM has a few tricks to extend his life (from the Lazarus project for example)
EDI and the Normandy - if survives the ME3, EDI+Normandy could be also a "recurring character" in ME4
Aria - she is also an asari, not young but not too old now, and Omega has a huge importance in the galaxy
So, there are plenty of options to use a lot of characters from ME1-3, I don't think there is a need to a direct connection with Shepard.