No, don't report every round, just report when something suspicious occurs, and it will be included in the Overwatch session along with rounds surrounding that point.
With Overwatch sessions, you get shown 8 rounds around the point that the player was reported, as people usually report after they felt something suspicious went on.
Each report is reviewed by multiple people, so if someone is reported many times I would work on the assumption that if the reports were close together they'd be covered by the same session.
Otherwise, if the reports don't coincide with the 8 rounds you see when doing Overwatch, say a report in the first round and a separate report in the last round, it may be split in to 2 sessions reviewed by 2 different set of users.
Either way, each report is added to the Overwatch queue.