see how-to-return-the-value-of-automatic-when-it-is-used-in-a-mathematica-function
Thanks to Bob Hanlon for this method:
p1 = Plot[Sin[x], {x, 0, Pi}, PlotPoints -> Automatic] Cases[p1, Line[pts_] :> Length[pts], Infinity] (*259*)
Another method due to Simon Woods
Trace[ Plot[Sin[t], {t, 0, 2 Pi}], HoldPattern[PlotPoints | MaxRecursion -> _], TraceInternal -> True] // Flatten // Union {MaxRecursion -> 6, MaxRecursion -> Automatic, PlotPoints -> 50, PlotPoints -> Automatic}