If the beads volume used was lower than suggested (normal), would the immunoprecipitation not work at all, or it will work but the amount of protein precipitated will decrease, and hence fainter bands when Western Blot is conducted ?
Yes, let's say antibodies in 20ul beads bind 1000 molecules, of course you do expect only about 500molecules with 10ul beads... dont you?
and using lower amount of beads is also tough to handle them during the washing steps(hard to pipette), so I would use normally 30-50ul beads at least.
I generally use 50 µl beads. Although a lower amount might be ok, it is easy to lose beads during the washes and if you start with very little already, this might compromise the comparability between samples (if you lose unequal amounts of beads for different samples).