Purpose of antibody wash
Two reasons for antibody wash:


To limit non-specific epitope binding. All ABs have specificity.  Washing is usually trying to remove weaker binding to non-intended targets.
For flow, excess AB that is not bound, if also pre-conjugated to a fluorophore, may allow for excitation of the fluorophore while going through flow even though the antibody isn't bound to the cell type of interest.


If you had a very specific AB, and very little excess, you may not notice a thing. I'm sure there are additional reasons; these are the two that immediately come to mind based on my own flow cytometry experiments.