In our lab, the treatments are done on adherent cells before detaching them from the cultureware. Conjugated antibodies or dyes are added to the cell suspension before flow. Hope this helps.
1. Addition of EDTA/Trypsin may affect the cell membrane thereby affecting the binding.
2. Anything that is bound on the receptor should not be easily washed away. The washing steps are essential to remove anything that has bound non-specifically. So whatever you are washing away is not what you want to acquire.
Darellynn's answer is to the point! You could also consider using a more gentle detachment solution like Accutase instead of trypsin which will not damage the surface receptors