Will ac compressor blow cold air if it has lost bolts

What is your question?

The ac was blowing extremely cold. Heard a noise.i looked under the hood, the pulley had a slight wobble to it. I drove 16 miles home, parked car, called AAA, they towed to the shop. According to supervisor the compressor was held together with wire and was about to fall off. Could this be the case where the pulley was the only thing needing replacement. The shop saw an opportunity for increased revenue.

What makes this problem better or worse?

Happened to quickly

How long has your 2010 Mercury Milan had this problem?

2 days