Technically, it would be equivalent the first day you entered early to DL. Your 4 day ticket would have an MM as part of it. So when you scan the ticket for an early entry to DL, my guess is it would register as an MM. Since you already have EMH as part of DLR hotel, then it is redundant that one day.
Here is DL 102: Some folks stay for maybe 2 days at a DLR hotel then switch to offsite. While staying at the DLR hotel, they get EMH every day including check-in and check-out days. So for 3 days. Once they switch to offsite there is no longer EMH.
But....
If they are careful to ask the CM to
not scan the MM off their entrance ticket while they are staying at a DLR hotel, then they will still have it available as a MM to use when they are offsite.