Well, possibly. It's all conjecture at this stage, but current climate knowledge (and logic!) would suggest that a weaker or diverted NAD would increase likelihood of blocking and, as we've seen in the last three winters (mostly in the north and west), an increased potential for PM outbreaks. Perhaps I was using hyperbole with my Newfoundland/Hokkaido comparison but given the predominantly cool and wet winters we normally experience, it wouldn't take much of a temperature drop to turn "cool and wet" into "cold and snowy".
Conversely, our winters could become stormier: two of the last three, I think we'll all agree, have been rather on the stormy side, and these have coincided with the pronounced cooling of the North Atlantic.
We're at such an early stage in our understanding of AMOC that all we can do at the moment is hypothesise, similar (in a separate but related (in terms how of they affect our climate) example) to our understanding of sunspot activity.