Yes.
So let's try out your idea with that verse from Luke.
You say the Father and the Son are the same person. Can the same person have a will and not have a will that is his own?
Example:
Bob is eating a bowl of ice cream.
You see Bob eating ice cream, and you say, "Hey Bob! Is it your will to eat ice cream right now?"
And Bob says back to you, "No, no. It's not my will. It's Bob's will that I eat ice cream!"
So you say, "But you are Bob, your will is Bob's will!"
And he says, "Nope! My will is not being done, but Bob's will is!"
Either this guy is crazy, or... he and Bob are not the same person!