Lots of talk on this by people who are really just guessing. BMW bypass vales recirculate into intake tract for one main reason: so there is no blow off noise.
Pulling off the hose and plugging the intake gives you the noise BMW and other car makers engineer out. There is no significant negative effects of this mod.
There is a slight one: BMW has calibrated the a/f on these cars to very tight tolerances. If you do the mod, your car will run slightly rich for a split second after shifting. On Audis, it would actually trigger an engine check light, but I've never heard of this happening on BMWs.
One solution would be to cut the hose and add a plastic T, so that you have the noise and still some recirculation.