ADC Selection Pulsed Measurement
Regarding your use of the pulse: good idea. Lets examine how long that pulse should be, if you want to measure the LED properties.

A cubic meter of silicon has 11,400 seconds thermal time constant. This is measured by uniformly heating one face, letting the heat flow out the opposite face, and insulating the other 4 faces.

A cubic 0.1 meter (10cm) is 100X faster, at 114 seconds thermal time constant.

A cubic cm is another 100X faster, at 1.14 seconds thermal time constant.

Notice all these sizes --- meter, 0.1meter, 1cm --- are much larger than the size of the LED junction depths.

A cubic millimeter is another 100X faster, at 0.0114 seconds (11.4 milliSeconds). This may be the size of the LED silicon, but what about the junction depth, right below that bond wire?

A cubic 0.1mm ---- 100 microns in size, or 4 mils, or 0.004 inches --- is another 100X faster, at 0.000114 seconds, or 114 microSeconds.

A cubic 10 microns is size is thermal time constant of 1.14 microSeconds. 

The 10 micron size may be about the accurate sampling window, if you wish to avoid thermal heating effects.