No, the lining of your uterus is NOT building up, higher and higher when you don’t have a period on birth control.  It’s just at a steady level which is usually smaller than your “regular period.” When you have a period off your birth control pill, it’s because you were building the lining of your uterus to accept an embryo – so you need lots of blood and nutrients.
When you are on the birth control pill, you aren’t trying to accept an embryo, so you don’t need to and you don’t build as much of a lining. and thus there is less lining to shed, when you do shed it.