Yes, dynamic integers are reevaluated every time you reference them.
What you want then is something like this:
integers {
s_code_1;
s_code_2;
s_code_3;
}
on_startup {
: set_integer var = "s_code_1" {(random(1))}
: set_integer var = "s_code_2" {(random(1))}
: set_integer var = "s_code_3" {(random(1))}
}