Doc - you have the stock power brake booster used in Little Thunderbirds - there should be no problem bleeding if all is functioning properly. Another issue is the unit may need rebuilding, which is a task I would let professionals do.
Based on my experience these units work well, but do not expect your Bird stop like a modern car simply because the brake shoes are narrow and the total swept area is much smaller than today's cars with bigger drums and disk brakes. No matter how well the booster functions, the original equipment's braking ability is not equal to today's vehicles - especially from 70+ (don't ask how I know!!
Since your car is modified with a newer engine and not concourse correct, I would like to suggest upgrading to disk brakes (manual or power). Several ways to go about it from scrounging parts in the salvage yard, to searching the parts counters at the local store, and complete conversion kits. If you choose a "kit" make sure it is complete and comes from a Thunderbird parts supplier, and not bargain priced incomplete kit from an unknown seller. Our suppliers know what works and have been providing a great service to us. My car has power brakes like yours but I used a complete manual kit from CASCO and I'm very pleased. Other suppliers have quality kits also. Yes there is more pedal effort, but the braking ability is greatly improved. Should I want to use the booster at a later date, it is just plumbed into the lines like you mentioned.
Enjoy the ride!