Consequences of $NP\subseteq P/poly$ to $BQP$
I'm not aware of any direct consequence of $NP\subset P/poly$ for $BQP$.  Of course it might lessen the interest in quantum computing, since it would mean that we could do something far more impressive with just good old classical nonuniformity than we could with quantum mechanics.  And it would imply $NP\subset BQP/poly$. :-)  OK, it would also weaken the arguments that BosonSampling, and other quantum sampling tasks of that kind, are classically hard.  For those arguments involve showing that if the sampling tasks can be done in classical polynomial time, then $PH$ collapses to the second or third level (along with several other strange things, like $P^{\#P}=BPP^{NP}$).  But if $NP\subset P/poly$, then $PH$ collapses anyway.