Does $P=PP$ or $P=PSPACE$ have consequences for algebraic class problem $VP=VNP$?

Question

Deciding majority of counting problem is $PP$ class.

1. Is there any relation between $PP$ and $VNP$ and is there consequence of $P=PP$ or $P=PSPACE$ to $VP=VNP$?

2. Is there a way to show $\#P$ is in $FP^{PP}$?

We do not know if $P=NP$ has an impact on $VP=VNP$ however how about $P=PP$?