100% true. The amazing thing is that Clinton’s program of “I am a woman. I am not Trump. It’s my turn.” already won the popular vote. Now imagine if they had a candidate who people actually wanted to vote for.
Edit: Data from here: https://ballotpedia.org/Voter_turnout_in_United_States_elect... (notably PA and WI are missing)
Maybe you could say states that transition from being safe to swing states see a turnout boost? I haven't checked. I would expect that turnout is more determined by demographics and inertia (states with high turnout in prior elections continue to do so, etc) than whether they are swing states, though.