The chances are remote.  You'd have to go through the tip of the root,
through the floor of the sinus and the sinus membrane.
    Generally, root canal filling materials are well-tolerated.  Of course
there is the potential of sensitivity to anything; still, any
sensitivity reaction would be local (in the tissue contacting the
filling--the filling would have to be overextended into the tissues) and
not remote, unless the filling was physically in the sinus or nasal cavity.

Steve

If you're allergtic to latex, you could also be sensitised to the
guttapercha points used to fill the canals. That reaction would tend to
be local. It's hard to see how it can cause post-nasal drip.
Which was the tooth that had the root canal?

This is purely anecdotal and mostly coming from "quack" websites.