While many people cannot hear the difference and the audibility will vary from speaker to speaker, you can measure the difference between the output of a speaker with the grill on versus the grill off:
Obvious different from the ACI Emerald XL speakers with the grill on and off.
hardly noticable difference with the Ascend Sierra 1 grill.
A clear difference with the AV123 Rocket RS250 speaker.
Clear difference, though less obvious, from the AV123 Mini Strata.
Dynaudio 110 measured grill effect.
Mordaunt Short MS902 grill effect.
SVS MBS01 version 1 grill effect.
Clearly something is going on. One could say they cannot hear the difference, but if it is measureable is could potentially be audible.
With all the audiophiles and geeks out there claiming they can hear the difference between two cables, between one power conditioner and another, between two amplifiers, or between two surround sound decoders where absolutely zero measureable difference exists, it seems to be we should take a very close look at the very clear and obvious measurable difference between using a grill and not using one.
Of course, the measurable difference is almost always in the midrange and treble, not in the lower midrange and bass. So using a grill on a lower frequency speaker is not going to be audible.