Hi Uncjat,
The walk between
Gare du Nord and Metro Poissonnière is
about 11 minutes according to Google Maps (on the street).
I'm not aware of any tunnel between Metro Poissonière and
Gare du Nord, although there is underground access between
Gare du Nord and Gare de l'Est.
If you're OK with rolling your baggage on the street, making this trip on foot rather than changing train lines will get you there in the same time or faster than the Metro. Have a look at the
Metro Route Planner and play around with the Advanced Criteria to see what I mean.
Ben