Correct if a train doesn´t need a reservation you just fill the traveldiary (paperpass) or add it to your trip in the Railplanner (Mobile Pass) and thats everything :)
However the direct trains Milan - Venice need a reservation But if you have time you can use 2 regionaltrains Milan - Verona & Verona - Venice reservation free :)
Yes you can just walk on the train. The Interrail/Eurail is your Ticket.
BUT
You have to write the train that you are taking (paper pass) or choose it on the app a(mobile pass).
Note: All long distance trains from Milan to Venice need an additional reservation on top (10€). When you take the Regionale Express to Verona and than the Regionale Veloce to Venice you don’t need the reservation (you need some more time to get to Venice).