Text: Matt. 8:25 (ESV)
"And they went and woke him, saying, “Save us, Lord; we are perishing.”
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A very good and original question, for it deals with an apparent illogicality of the question: if the disciples think that the boat is to sink, then it will sink with all aboard, the sleeping Jesus included, for it is absolutely counterintuitive that the disciples entertained an idea that the boat would sink with all of them together, except for the sleeping Jesus, who would not sink in some miraculous way. However, the gist of the illogicality is that they definitely have a hope that Jesus while awake can in some way or another rescue them.
All this has to do with the incompleteness of the disciple's faith in Jesus: they still do not understand that Jesus is the very Logos of God, who governs all natural processes, who, while sleeping according to His human nature, is eternally "sleepless" along with the Father. Thus, the disciples think in their incomplete way of Jesus as just a prophet, or even more, the Christ, the Messiah, but still just a man, who can help by his intercession and prayer to God only while awake and not while asleep. Similarly, the Jews thought that Jesus can heal the ill only if He would approach them physically, but not from a distance, while the wise centurion intuiting the Divinity of Christ, asked Him to heal his servant from a distance (Luke 7:7).
That this is so, is seen in the continuation of the story: Jesus wakes up, condemns their little, incomplete faith, and then orders the natural phenomena to calm down, which the latter immediately do. The disciples are then driven to a bewilderment: "Who is He, whom the sea and the winds obey?", of course remembering the Psalm 89:9 "You rule the swelling of the sea, when its waves rise, You still them", and this they see Jesus does, and does not through any prayer to God as a prophet or a servant, but out of His own sovereign authority, as God. Thus the disciples' question can be worded as: "Who is He, if not the very Lord whom the prophet David addresses, if He immediately subjects the winds and seas to His sovereign authority?" For sure, after this instance, the disciples were meeting with a calmness of spirit all tempests of the sea, even while their Teacher was taking a nap on a boat.
Thus, in "we", of course, Jesus is included, yet, only in His sleeping stage, for in their incomplete faith and understanding of who Jesus is, the disciples have a hope that if awakened - and only if awakened - Jesus can rescue them through prayers to God, who would listen to him as to a righteous man and a prophet.
A question may follow: but if they speak to Him, then He is already awake, so do they still include Him in the "we", for they definitely also hold a hope that He is able to rescue them? Given what was said above, I think, still yes, they think that they all may perish unless Jesus does something, prays to the Father and asks for rescue of them all, with a great hope, but perhaps not 100% calm assuredness, that God would listen to Jesus.
From this we can infer that there is not a single moment when Lord does not care for us and this knowledge should be in us not theoretically, but existentially, helping us to gradually overcome the fear of death, for any tempest and even death is incomparably less fearful than losing or lessening of our faith in Christ.