Nope, that is not what it does.
First, sin(x) ~= x for small x. Second, 1000.../555... = 1.8. Neither of these have anything to do with pi. With these in mind, the program can be simplified as
The main and only reason you get pi in the end is that the radians function is defined as radians(x) = pi * x / 180, which requires knowing the value of pi to begin with.
So this program is basically an equivalent of
multiply_the_argument_by_pi(555) / 555
except with a few layers of completely unnecessary math on top of it to obscure the magic trick.
So this program is basically an equivalent of
except with a few layers of completely unnecessary math on top of it to obscure the magic trick.