I have to agree. The worse time for most regulators is Turn-on, and you would be turning it on and off many times a second. Even if it "worked", it seem like you would be shortening the life of the regulator, and causing reliability issues. A much better idea of course is using the PWM output of a Arduino. It shouldn't be hard to find, or just create, a simple sketch, but you will need some switching circuitry (transistor-ish), because the Arduino can't handle the LED string's high current 12V. But you could get help here from Adafruit.
If you are really adverse to using Arduino, I have seen DIY LED dimmers using 555 chips. Just Google 555 LED dimmer. Bad news is this would be without Adafruit support.
Lastly there are manual dimmers made for LED strings. Again, just Google PWM LED Dimmer. Amazon has one for $10, and they even show something of a hack on the product page.