No it wouldn't. Or rather $::row would revert to whatever it was before you localized it once you exited the sub that contains the localization. In the example below i use a bare block instead of sub to demonstrate but the same thing applies.

D:\dev\PM>perl -le"$::x='outer'; $c=sub{print $::x}; { local $::x='inn
+er'; $c->() } $c->()"
inner
outer
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Thats the whole point of dynamic scoping...