Possibly. Vibrations set up in the engine could cause accelerated wear. If the main pulley fell off you would lose the function of all the engine accessories.
it should be o.k. if you drive it in a demolition derby , but not for daily use
If the balancer comes apart it possibly could damage the engine or related parts. Don't drive it, get it repaired.
Where can I get my 1962 balancer rebuilt?
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