It's been about 2 years since I attended an e-night while staying at a Downtown Disney hotel (Grosvenor) but I believe the same transportation was running that was running during the day. At that time the Grosvenor also participated in the early entry and the buses started running early.
I'm going in June and plan to attend at least one e-night. Like LoveToDisney said, we can always take the bus to Downtown Disney and walk to the hotel. Thankfully the walk to the Grosvenor is shorter than the walk to the RP. Of course there is always the bus from Pleasure Island to the hotels.
I just can't imagine them participating and not making arrangements for transportation.
Carolyn