ORIGINAL: Franklin Nimitz
This is why I think they should list radios and maybe wire gear as equipment. Only units with functioning comms gear (some radios only function when a unit has basics (i.e. batteries)) should be able to call in artillery.
Radios weren't the only tools that were used to communicate with arty assets, though. Especially on fixed frontlines, the Germans mostly used their field telephones to call in arty support, but even with moving frontlines, field telephones were still widely used. For instance, German Infantry Gun Coys employed a radio car (in order to communicate with the forward arty observer), but also a car with a switchboard hosting a telephone exchange crew. In addition, motorbike messengers (Kradmelder) could be sent in order to establish contact with a line company's arty liaison officer, or with the Bn/Rgt commander.
The messenger system was used all through the war and used by Army and SS, either as backup system or to maintain a certain level of secrecy (eg. when setting up the offensive in the Ardennes).
That said, the Germans did not need radios to call in and receive arty support.
I don't think that US/British forces were using field telephones often, but I know that they had employed runners or messengers as well, occasionally at least.