Schematic: http://www.nostalgiaair.org/Resources/v ... 011828.pdf
It's a complicated setup, but I would say yes, the loop needs to be connected for reception on the broadcast band, whether or not an external antenna is used.
The loop antenna has two parts, referred to in the diagram as primary and secondary. The primary is just a turn or two that serves to couple the external antenna to the secondary when on the broadcast band. If the loop antenna is missing or disconnected, the signal from the external antenna has no way of getting into the radio.
In the shortwave bands however, the bandswitching sends the external antenna signal in via a different route and not through the loop antenna.
It looks like you're going to have to trace out the wiring to ensure the loop connections are correct. Incorrect connections could certainly cause the symptoms you describe.