Due to the typical field of application of visible LEDs, their datasheets generally do not specify switching characteristics (like it happens with regular diodes or IR LEDs). However, from the electrical point of view, you could assume that they are fast enough for the application you describe (for high power LEDs, typical turn-on and turn-off times are in the order of tens of nanoseconds, but achieving this level of performance requires careful driving techniques).
With that in mind and, IF your application uses monochromatic LEDs (includes IR), then you could assume an optical switching performance similar to the electrical switching (light emission is proportional to the LED current). This means that, with relative ease, you could achieve an optical switching frequency in the order of 10 kHz, or even more depending on driving techniques (for your reference, optical modulation on common IR remote controls tipically operate above 30 kHz).
However.... if your application requires white LEDs, then I'm afraid that the response time of the phosphor coating is much slower than that of the LED itself. Whether it is fast enough for your application will depend on the maximum operating frequency you need. Unfortunately I have no data on phosphor performance.
If you need a really fast white-light strobe frequency, maybe you should consider using mixed color LEDs (RGB) instead of phosphor-converted white LEDs.
Regarding continuous operation, if the maximum electrical operating limits are respected (peak current, pulse width, duty cycle and heatsinking), then it should be possible to attain the full lifetime specified by the manufacturer (typically about 50000 hs, depending on the LED, but phosphor based LEDs age faster, though).