There are various ways you might look at this question, but an easy one is to look at scoring averages for teams after they play an OT game and see if they differ significantly from the scoring average when they haven't just played an OT game. Ignoring neutral court games, I looked at how many points home teams scored and gave up for both cases:
|No OT||After OT|
As you can see, there's a mild effect, particularly on the defensive side of the ball, which totals to about 1 point difference in MOV. There are about 1200 games in my database that meet the "home team's last game went to OT" criteria, so this isn't a huge sample.
For what it's worth, since 2009 there have been 11 Tournament games where the home team's previous game went to OT. In those games, the home team averaged 69.5 points and gave up 65.5 points.