Chances of a room at DL Hotel almost same-day in June?

I'm thinking about doing the following:

It seems very hard to book a vacation package at Disneyland Hotel, from the USA, with decent rates, so I may go ahead and start my visit with several nights at an offsite hotel.

However, I will be buying a dream fast pass.

On my first day there, with my dream fast pass, could I walk into the Disneyland Hotel and ask them to book me a room for my final night 3-4 days later? Would a Tuesday or Wednesday in June for example be likely to have a room available, if I asked for this say the Friday before? Does the hotel take a reservation in person like that and with a dream pass I could get it at slight discount without park tickets too?

I just thought this might enable me to finish out my stay's final night at the DL hotel. I could have a backup reservation back at my off site hotel, if this fell through.

Any thoughts? Many thanks.