As in, drain to +V, source to -V, gate and source to PWM...?
If it's truly a "constant current source", this is the proper way to do it. However, I'd be surprised if it actually is, because CV supplies are so much easier to build -- usually there's feedback (with a low bandwidth) controlling the average current level, but the actual output is bypassed with capacitors and stuff so that it's not also an AC current source. Which means the frequencies in the PWM signal won't be treated too kindly, and you'll have problems.
It also means using a series switch is problematic. Yes, you can turn off the LEDs and be absolutely sure that they'll be off... but for how long? Ideally, a current source climbs to infinite voltage when open circuit; the power supply likely has an overvoltage protection in it to limit this, but the flipside is, when the PWM turns on again, how long does it take before LED current is normal? You'll get a huge inrush as the voltage comes down from limit to nominal. Or the supply shuts off and goes into an intermittent state, and takes time to recover.
A better option is to simply get a supply that has dimming control available. If this is more expensive, so be it. You could also try hacking one to make it dimmable, but without the circuit, obviously we can't give direct advice.
Usually there's a summing node, where the current feedback signal goes into a controller. You can add current from a resistor divider -- coming from direct or filtered PWM -- to fake it into thinking there's more LED current than there actually is, and therefore throttling down. Beware, you may have to do this from the AC line side -- and the controller being self-powered, means if you throttle down too low, it loses its own power and it starts blinking. That's one [accidental] operating mode of an
LED light I made for myself, when turned down too far.
Tim