No. We stayed in a suite in January, and it did not come with club access unless you paid an extra $250/day!! The exception is the Signature Suites. They do have club access but they also cost an arm and a leg.
Our suite was super awesome, though. We were on the 14th floor of the Frontier Tower with a view of the pool and parks. Great fireworks viewing and we had 2 balconies with furniture. There was a wet bar with stools, mw and larger fridge. We have done club level from regular rooms and that's a decent deal if you have 4 or 5 people, but adding $250 to a suite for concierge is ridiculous IMO.