Is the special servitude, which includes everyone who worships Allah according to His law, inclusive of disbelievers if they perform something from the branches of Sharia as an act of drawing closer to Allah, given that they are addressed by the branches of Sharia?

The specific servitude mentioned by Ibn Al-Qayyim is the servitude of obedience, love, and following commands. A disbeliever does not enter into this specific servitude for two reasons: First, because he supports Satan against his Lord, as stated in the verse: "And ever is the disbeliever an assistant against his Lord." Second, because the deeds of a disbeliever are not accepted from him as long as he persists in polytheism, as stated in the verses: "But if they had associated others with Allah, then tremendous loss would have come to nothing from what they were doing," and "And what prevented their contributions from being accepted from them is only that they disbelieved in Allah and in His Messenger," and "And We will approach what they did of deeds and make them as scattered dust."