The exact route matters. Where are you flying from and to?

Correction - my information is old, and Delta has changed the language of the policy. Previously, only certain flights to JFK qualified. Now, any domestic flight branded as Delta One qualifies.

The good news is that if you are confirmed in advance with an RUC, you will definitely get access to the Sky Club, because you have "paid" for your upgrade with a certificate. My old impression was that complimentary upgrades don't get access, but instrument upgrades do; this may have changed recently, because I can no longer find language saying that on delta.com. But an RUC should work regardless.

Either way, you wouldn't have access until cleared into the Delta One cabin, so if you were waitlisted, you wouldn't get access until the upgrade cleared - which wouldn't occur until T-45 minutes or so, past the point at which you'd be able to access the club.

I'm not sure the policy on connecting flights beyond the Delta One flight. But given that they explicitly call out connecting flights for international trips but not domestic, I would operate on the assumption that the answer is no, and be pleasantly surprised if you ask and are admitted on the day of travel. Can't hurt to politely ask, though!

Have a safe trip!