Does intravenous immunoglobulin (ivig) infusions benefit someone with IgG defiency?

Possibly. If you are deficient and symptomatic (recurrent infections), they can possibly help your body fight infections better. Just because you have an igg deficiency does not mean your are immune deficient, however. Many people with low numbers have normal function and really are asymptomatic.
Yes. If your IgG is clearly low or is not functional(ie low antibody response) then replacement IgG to get your levels above 1000 would be helpful. .