There are cooling jets underneath each piston close to the crank and aligned to centre of each piston . Not sure if the closest one, could reach the balance shaft recess - only if the recess is not fully closed and has an open gallery area to the crank area below.
Looked at the VW Self Study Guide which has some good diagrams of oil supply and return schematics and of the balance shafts and chain and tensioner but doesn't show or touch on the plastic tube....
Spent a bit more time looking at other videos this morning, got no further really. On the gen 2, there is quite a few balance shaft seizes out there on golf GTis and the like. All that I saw videos on - are on the exhaust side. On the gen 2, on the bs it doesn't seem that they ran the needle roller bearings now present in the gen3, but they still had a plastic tube on the exhaust balance shaft....
One of the videos I saw, with a siezed balance shaft, had damaged the plastic sleeve melted and distorted, from heat due to a strainer oil intake mesh on the balance shaft being partly blocked. Assuming that is the correct order of events. It's one hypothesis. It hadn't full broken apart though - the tube on that video it, the engine seized solid after a dyno run. And for the plastic parts that size to get to the bottom of engine like in this case, maybe there is a void or big return gallery in that exhaust balance shaft recess open to bottom of engine.... The debris can't come out the front of the balance shaft its bolted - to block. The debris size couldn't travel by fine oil galleries..
One worry I'd have is that the plasitc tube has failed due to excessive heat - due to a starved bearing on the balance shaft which could present a balance shaft failure risk without addressing..
The other, is whether that sleeve is directing oil or retaining oil in a particular way to ensure reliable operation of the balance shaft.
Admittedly, it is expensive to address any of this and it seems to be running well for time being, so is it worth it on a fairly high mile vehicle....
It's all got a bit over my pay grade. And my head hurts now. I may post a comment on one of the gen 2 video failures I've seen and ask what they see the plastic tube purpose as...... see if I get a bite...