Originally Posted by GBadger

In theory it's not allowed, so they may turn you back. The access rules for SkyClubs were recently updated to include:
Originally Posted by delta.com
Members can only use the Club in conjunction with same-day ticketed air travel but such travel may be on any airline.


So, in theory, if you're not flying, they can deny you access. Depending on the location, they may or may not.