I'm used to working on cars, so I might stand corrected when it comes to bike stuff.
However, from what I know, the point of having a tube that goes from the crank-case to the air-box is for the suction created by the air intake to also create a vacuum in the crank-case, which helps with piston ring sealing and draws out oil vapors/emulsions created by the rotation of the crankshaft. On the stock Rebel there's an air-oil separator that condenses the oil vapors and sends them down the puke tube, allowing only clean air into the air-box.
On old-school performance cars it is relatively common to delete the PCV system (the automotive equivalent to this), but there are some trade-offs:
By removing the system, the piston rings won't seal quite as well and the engine will experience more "blow-by" leading to a slight loss of power (in cars this is usually largely compensated by the power gained from a more free-flowing intake). Note that on a bike, since the intake faces away from the direction of airflow around the vehicle, the stock air-box may or may not be better at channeling air into the engine than an open intake, I have no idea.
Long-term, the increased "blow-by" may wear your piston rings a little bit more, and retention of crank-case vapors may incrementally affect crank journal wear.
There should be limited harm in sticking a small filter straight on the crank-case, provided it is free flowing enough to prevent buildup of positive pressure, but prevents dirt and particulates from entering the engine. A step up from that would be to run the tube to some other vacuum source (I've seen things like exhaust bungs, but they do have draw-backs).
To summarize, by removing the air-box and crank-case vacuum, you're trading a bit of longevity for better looks, lighter weight and perhaps more power... (provided you put good enough filters to keep dirt out of your engine). Whether the small amount of increased wear will cause an engine failure before any other issue does is anyone's guess.
Sorry for the long post.
1985 Rebel 250 (in blue of course).