If I have a 68/73mm BB in my toolbox and need an 83mm one, can I just ditch the plastic tube that goes between them?

yes

So why is there the sleeve there?

to keep the shit out the bearings from the seat tube/hole in bb shell etc

Ok, thanks.

If you want to keep it in, just slice the plastic tube in half, and then extend it from the middle out. Use something like the thin metal from a coke can and wrap it around a couple of times, then a bit of electrical tape to keep it in place.

or just tape cling film over the cut ends