Most plastics have a specific gravity very near that of water. This means that most plastic will barely float, barely sink, or suspend mid water column. You will want something to weigh it down, otherwise it's highly likely to move on you.

Are the culverts double wall corrugated? If so, I would cut/drill many holes on each rib to help it waterlog. If it is double wall...the ribs may be a good place to pour some wetted sack-crete in to weigh them down.

Fish on!,
Noel