Is it a true experiment if you have two IVs; one which includes random assignment and one which doesn't?

For instance, a 2X3 factorial design comparing gender and three treatment conditions?Is it a true experiment if you have two IVs; one which includes random assignment and one which doesn't?
A true experiment is one where you are manipulating a factor- so yes, two IVs counts. Also, the IV cannot be quasi-independent variable (like gender or age because you are not manipulating these, even though you might be studying them)