Without that delay valve when you press the brake pedal your front disc brakes will engage before your drum brakes apply, if they ever apply. That would place your braking bias on the front brakes. In wet conditions and in high speed braking you may have a serious disadvantage over properly metered four wheel braking.

It's easy to check the delay valve on-car; when the brakes are applied, the little button on the back moves out. If yours would not move in, are you sure you did not have a residual valve or check valve in your line lock or in your master cylinder to allow brake fluid to return freely up the line?

I think you only have to depress that button for bleeding when you are using a pressure bleeder at the master cylinder or the pump-the-pedal method, not with a vacuum or gravity bleed. I did not have to depress it for a successful vacuum bleed. The first time I bled them after replacing the lines and master cylinder, I bench-bled the master cylinder and filled and capped it, then used the vacuum bleeder to fill all the lines from a bottle, then attached the lines to the master cylinder. This dramatically reduced the number of trips from the underside to the engine compartment to refill the master cylinder. Final bleeding was very quick and easy.

Jim's suggestion for opening all four bleeders and seeing if you get a squirt from each corner is valid. If you have a kinked hose or line or other obstruction you can bleed and bleed and never overcome it. Fluid should squirt freely from each bleeder screw with a single press of the brake pedal. Unless you have a helper to close the screws while the pedal is still down you will need to bleed again.