Yes - cutting it back that hard will actually rejuvenate the plant in a literal sense. You'll get an explosion of back-budding if the plant is presently growing with good vitality.

Al

I planted a Rosemary by the gate, said to protect you & bring good luck.It was too big, so I cut it back & gave fresh limbs to my family too use. My brother striped the leaves & dried them & keep the wood to burn when he grills.
That was 4 years ago & the plant is bigger now, then the day I cut it.

Thanks, I'll do it today. :)