If the alignment has been out for some time, then the tires will have worn unevenly. That can cause vibration. By itself, alignment doesn't usually cause vibration. Being out of balance can cause vibration, or something loose in the suspension.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue