If you search the boards, or tripadvisor, you'll find that Eden Roc is not a popular choice. If you're just looking to save money, I'd go through Priceline before booking Eden Roc unless you are 100% okay with mold, peeling paint, bugs, stained carpets, hair in the sinks, etc. (just reading a few of the most recent tripadvisor reviews).
If for some reason you still decide to stay there, you would be able to go up and through DTD to enter the parks, but you wouldn't be allowed to cut through the GCH entrance, at least not in the mornings.