"..... and possibly elected to continue and fly the damn thing around the circuit without the ASI which I imagine would not be much fun."
Why?
Power + Attitude = Performance
This should get you safely around the circuit in most GA aircraft.
The last time I had to deal with no ASI was in my first flight in an A36. On T/Off the ASI came up to 70 kts - and stayed there for the entire circuit.
Personally, I think that demonstrating the ability to successfully fly a circuit without ASI should be a requirement for a PPL (or whatever its called these days).
Dr 