Not their entire suite, but Photoshop Elements and Lightroom are in the Mac App Store. You can even buy a subscription to Lightroom with in-app purchases.
And of course Adobe has many apps in the iOS App Store.
But you don't need to have your iCloud mail set as the primary mail for your AppleID. You don't even need to create an iCloud mail when you create an iCloud/AppleID account, it's an optional step. I recently created another iCloud test account and it's also not shoved in your face or anything, it's a small little button called "Don't have an email address?" somewhere.
So I don't even really understand how people get into this situation.
