Most of the CV drivers we use are also CC until it hits their max voltage (36v, 42v, etc). So as long as your COB draw less voltage, your driver is running on CC mode. A true CV driver wouldn't work that well for the way we build.
COBs draw current, not voltage. Voltage is applied (or dropped), and current drawn.
Actually pure voltage regulated supplies work quite well for parallel loads. I've got two in my closet humming away constantly for the last four months. I can adjust the voltage on them from 25 to 42 volts and it stays rock steady regardless of current draw. Current stays around 8 A (max is 11 A), fluctuating slightly (+/- 200 mA or about 30 mA per cob) depending on temps.