No, because the T-Stat housing is almost the highest point of the engine. And The Water pump creates flow, not pressure. You are not going to see much fluid coming out.
Just install ur New T-Stat, bleed the cooling system, and go test drive the car.

 

Well the T-stat was not the culprit. I also found out boiling a t-stat is not a fool-proof test method. A T-stat also needs pressure to open.

Anyways, I have service records for the van and the water pump was changed but it had a plastic impeller. Mercy. See what I found?

I could not find the other pieces.

 

I hope ya found the other pieces. I leave the pump off. disconnect the hoses for the top and bottom. use house and try blow out the pieces if you can.. hope that helps.