U is velocity, yeah.
Continuity holds for anything, that is mass flow rate in = mass flow rate out.
If the area of the larger pipe appropached infinity, the mass flow rate in would be infinity + the mass flow rate of the smaller pipe, which is negligible. So the mass flow rate out, downstream, would be infinite (the mass flow rate of the larger pipe.)
Of course none of this takes into account viscous effects etc.
Imagine a duct outside of a car with no other purpose but to slow air coming in and through it. What happens to that air on the otherside of the duct? Speed up?
Effectivly yes, in reality it's so tiny as to be negligible. In reality, turbulence around the pipe would probably slow the air around the pipe down more than continunity would theoretically speed it up.
Your bone's got a little machine