OK, not the Awake!, but in Consolation, it's predecessor. Refer to this thread: http://www.jehovahs-witness.com/10/128918/1.ashx
There appears to be a "dirty joke" in the first issue (November 29, 1939) posted in the thread. A limerick is printed on page 2 under the heading "Equ Seau", amongst other "entertaining tidbits":
There was a young lady named Fleau,
She had a good-looking beau.
Said Fleau to her beau,
"Let us geau to a sheau."
Said her beau, "If you'll bleau, Fleau, I'll geau."
Did asking a girl to "blow" have a different meaning back then in 1939, or did they publish a dirty joke, inadvertently or otherwise?!?