The rules for Sky Club admittance for those with a Sky Club membership require a same day boarding pass. It does not have to be on Delta.
http://www.delta.com/content/www/en_...use-rules.html
In practice, they don't typically ask for a BP. If you are not flying at all, I wouldn't count on getting a gate pass just to access the Sky Club as you are not entitled to access. There are some that will buy a refundable ticket and then cancel to get access when not flying (although, technically, any fare should work if you buy within the risk-free cancellation window).