Carl was arrested for evading the draft backstage at the April 26th, 1967 Long Island gig after refusing to attend his draft board in LA on January 3rd the same year. He missed the first show of the European tour (Dublin, May 2nd) because his bail was being sorted out.
Next question.

Which of course proves that the witers couln't have been thinking of Carl Dean Wilson when they wrote the script?
Nah, I'd say your guess is as good as mine.
>> "In 1966, during the Vietnam war, Carl Wilson received notice that he was being drafted into military service and was ordered to report for duty on January 3, 1967." <<
The Carl Wilson from Green Acres could be anyone, as you stated, but being a LA created program, and Carl being well known in the area, I'd say it's just as safe to argue they were thinking of "our" carl. ( tho it doesn't really matter, I suppose)
Perhaps someone can track the script writer(s) and ask them?