I haven't found anything in the literature that suggests what would happen if that is the case. Thank you, Akash
$NL=P$ is not considered likely by the experts.
The corollaries include:
$P\subseteq L^2$ by Savitch's theorem
$NC=P$ by the Squeeze theorem
$EXP=PSPACE$ by $P\subseteq polyL$
I would like to include or exclude $P=L^k$, $k\in[1,2]$, but I have not collected sufficient evidence for or against that conclusion.