"Somewhat" dim memory was evidently an understatement; turns out I was wrong.I don't have any data on this, but my understanding is that these parts exhibit significant afterglow, lasting on the order of many microseconds up to several milliseconds. IIRC, I've read they have a complex afterglow "tail" since the white color is obtained by a mix of phosphors, each having its own decay characteristics. (Caveat: this is all secondhand info, unverified and cited from my somewhat dim memory.)
I took a PIN photodiode, put it in series with a 1000Ω load resistor and gave it 10V of reverse bias to reduce its capacitance, then illuminated it with various red, green and white LEDs driven by my pulse generator while observing the voltage across the load resistor with my oscilloscope.
The red and green LEDs gave output rise and fall times of around 100 ns. The white LED (not a high-power illumination-type LED, just an ordinary 5 mm indicator type) showed rise and fall times of about 200-250 ns. But there was no observable afterglow from the white LED on any timescale-- nanoseconds, microseconds or milliseconds.
Santa is bringing me some 3 watt white LEDs to play with, and once we get past Christmas I'll rig up a high-power driver for them and give them a try. I'll also put together a fast transimpedance amplifier for the PIN photodiode which will hopefully take any detector speed limitations (like stray capacitance across that 1000Ω resistor) out of the picture.
But for now, the bottom line is it appears I was wrong about that "tail."