Branch on ?: operator?

For a typical modern compiler on modern hardware, will the ? : operator result in a branch that affects the instruction pipeline?

In other words which is faster, calling both cases to avoid a possible branch:

bool testVar = someValue(); // Used later.
purge(white);
purge(black);

or picking the one actually needed to be purged and only doing it with an operator ?::

bool testVar = someValue();
purge(testVar ? white : black);

I realize you have no idea how long purge() will take, but I'm just asking a general question here about whether I would ever want to call purge() twice to avoid a possible branch in the code.

I realize this is a very tiny optimization and may make no real difference, but would still like to know. I expect the ?: does not result in branching, but want to make sure my understanding is correct.