You'll need ski crampons at a minimum and July is likely to be sun-cupped and challenging going up and down. Spring conditions are often tricky for skinning, let alone your first time. It really depends on how the spring shapes up. Some years Adams could still be an OK ski, but others it might be terrible.
Typically, once July comes, I put the sliding gear away. I actually think walking in July is more fun and not much slower, if at all (since you're traveling lighter on the way up). If you can move the trip to late May or early June then it is a different story.