Storing output in a parameter

Yes and no. And it depends on what you want exactly.

NO: @getdate won't be a parameter, it will be a variable
NO: it is not wise to declare a variable with the same name as a function in the same context
YES: you can declare and use variables
YES: you can store the output of a function in a variable
YES: you can retrieve value of such functions, like this: select getdate()
YES: you can store output of a function in a variable: declare @date datetime; set @date = getdate();select @date;
YES: you can retrieve DAY value from a date
YES. you can even store a day value in a datetime variable, but it is nonsense.

So, it would look better this way:

declare @date int
set @date = DAY(getdate())
select @date