IIRC , Chevy had done away with the two piece radios by 1954 but it could easily have been a high end (better quality) aftermarket unit .
It uses a vibrator to boost voltage up for the plates in the tubes , the points tend to stick every so often and the bouncing of the truck popped them loose , is why it came on ~ that's the faint humming sound you hear when you switch on a vintage tube typ car radio .(the vibrator working)
I'd say yes , it is worth keeping , replace the speaker with a _matching_ ohms one ASAP to see how well it works , then figure out if you want to have it rebuilt or just keep it working , self servie is easy , remove the case cover and look for the big ftall topped aluminum tube looking thing , that's the vibrator , it'll have either 3 or 4 pins and they now make replacement ones that are transistorised and ground specific , the old ones bon't care about polarity . if you're on a real budget and it stops working , carefully pry off the cover and run some stiff lint free white paper between the points to clean them up , this fixes 95 % of vibrator troubles .
Write down the tube #'s and get some N.O.S. spares off E-pay or other old stuff site , they only cost $5.00 ~ $10.00 each and many older TV repair shops will have them sitting on the shelf...
Having it rebuilt is better as the capacitors are crummy quality (old tech) and should all be replaced to protect the rest or the radio from burning out should one fail catastrophically .
Enjoy ! .