I tried to connecting the opposite borders just as proof of concept, it works, but then the rest of the pieces becomes very harder to loop or to connect from side to side.
The idea is interesting but I don’t think it is well thought out. For example, right now I don’t see why you would place the 1x4 piece vertically unless you absolutely have to. I am guessing that most of the pieces had to be oriented to a certain way which limits the decision for the player. There may be potential here, but the pipes mechanics should definitely be reworked.