I keep hoping some one with a 1996 FSM will chime in on this.
The 94-95 is different from the 96 but they are a Bosch 2u system and should be similar.
If your engine/exhaust system is not too loud you can check the pump by ear.
Find a quiet downhill spot. Turn the car ignition to off. Then start the car and let it roll down the hill. At 4 MPH you should hear a short buzz of the ABS pump doing it's "Auto Test" (automatic test). If you are sure that you can turn and stop the car with the engine off. (no power steering and no power brakes) you might hear it better (key in run ). It sounds a bit like the fuel pump noise you get when you just turn the ignition switch to run. Buzz stop.
The ABS system does this every time you start the car and get it over 4 MPH (fwd or rev). If the pump or valves failed electronically The ABS light would be turned on and they would have a fail code to read.
The 1994 system with the correct dealer/aftermarket scan tool can go Mode 4 (misc. tests). Some one who knows what they are doing will be able to do the "Auto Test" with the car standing still. The valves can also be checked.
Dealership says they used their equipment to bleed the ABS system and couldn't get it to bleed. Is this any indication that the ABS PUMP is dead?
No, the pump and valves are one unit and will be replaced as one piece. It would take pages to discuss how they decided "couldn't get it to bleed" The short question is why there is no ABS trouble codes if they were really unable to move the valves. To be fair there are failures like yours that do not trip a code.
Now for a short rant. I would not let these guys oil the chain on a pedal car. They do not seem to understand ABS systems. The ford system on my crown victoria does all the same things all the same way. I have had to read the Chevy FSM to make sure I am not confusing the two. My personal opinion is they do not know how to use the correct scan tool or do not have it. When you fix it get a report from the shop. Get a couple of 6 ft friends and have a talk with the dealership's general manager about getting some of your money back.
I would talk to some other repair shops and find one that show you the "Auto Test" triggered by the scan tool. I still think pressure gauge will lead you to replace the ABS module.
I almost never recommend "just tossing parts at a problem" In this case it might be cheaper for you to install a junk yard ABS module then have a shop that can do a ABS bleed finish the problem. You would know you were on the right track because the brake pedal would not go to the floor.