How does :Disconnect() work and can it be used on a disconnected event?

Recently I was writing some code that would disconnect two arrow buttons if the screen was cleared. Because the clear button can be clicked again before the events are connected again, I decided to use a boolean variable canDisconnect that is set to true when the events are connected again. Here is an excerpt from my code:

local db = true
clearButton.MouseButton1Click:Connect(function()
	if db then
		db = false
		if canDisconnect then
			connection:Disconnect()
			connectionTwo:Disconnect()
		end
		clearScreen(frame)
		wait(5)
		db = true
	end
end)

One of the events that changes canDisconnect is this one:

connection = rightArrowButton.MouseButton1Click:Connect(function()
	canDisconnect = true
	if db then
		db = false
		if pages[pageNumber.Value + 1] then
			print("there is another page")
			pageNumber.Value = pageNumber.Value + 1
			loadPage(pages[pageNumber.Value], frame) 
			getIngredients.OnInvoke = function(name)
			--code					
			end	
		end
	wait(1)
	db = true
	end
end)

It would be much better for me if I could use :Disconnect() on connection even if it has already been :Disconnected. This leads into the second part of my question. How does :Disconnect() work? I know what it does, however, I don't know how it works. Does it set connection = nil? For some reason it does not seem like that would work. I would appreciate any insight in this matter. Thanks!