I am getting a vibration when the drivetrain is under load. Is it possible for a bad axle to cause this, even if it doesn't give the normal clicking sound when turning?

I looked under my car and there is quite a bit of grease around the boots....

 

if theres grease around the boot, its torn or bad.
im going through the same thing with my b16 right now
its spitting grease from the boot
taking it off in about an hour.

 

I know the axles need to be replaced - I was just trying to figure out if thats gonna fix my vibration problem.

 

Could be the inner CV joint going.

When the outer joints go, you'll hear that clicking sound when you turn the wheel. When the inner ones go, you'll frequently get a shudder or vibration when you accel or decel.