Superficial Tension

Yes it is possible that air is trapped in the cavity. I would use a little vacuum followed by pressure to ensure that the air is displaced. ( Much like vacuum - pressure impregnation used in electric motors)

Arjun

Are you submerging the whole piece? If you are then why can't you turn it 90 degrees and leave it at that or have it rotate while submerged. If your not submerging it then could you have a pump and direct the flow at the boss? I am not sure if that would over come the tension, but it is inexpensive.

Coating inside high-aspect holes requires control. You could try to inject at the bottom it using a metered syringe. You could then spin the piece or blow into the bottom to cover the sides. The level of control you need will depend on whether/how the primer wets the sample.