Jason8102-
If the tank has to be filled with water, but there is not means of venting the air, then the design is poor. If it is small enough, I'd suggest turning the tank such that the filling opening is up and pouring the water in and letting the air vent out.
What worries me is your assumption that the hose will put out 3 psi. That is more than an order of magnitude off from typical US residential plumbing. Depending on your system, you should expect to see between 40 and 80 psi. If you leave the air in the tank, you, as you suspected, will have a mix of air and water both at the hose pressure of 40 to 80 psi. Now, with a large volume of air at 80 psi, depending on the design of the tank, you may have a hazardous situation. There's a reason we don't usually do pneumatic tests.
jt