Bad Diff Bearing Vibration

[Zeke]

I have a 2007 silverado new style. I had my local mechanic do an alignment and he noticed that one axle boot was torn so he suggested replacing the axle which I had him do actually I had him do both sides. I went to have the alignment because of a weird vibration in the steering wheel not a shimmy but a slight vibration that is constant at all speeds. He noticed that the flange that the axle bolts onto to that goes into the diff on the drivers side has play (up and down) in it about 3/16" maybe a wee bit more. Would this cause the vibration I am having in the steering wheel?

[gmtech4]

no