THE ANSWER
No. Laser needs pigment in the hair to work, and white and grey hair has little or none left. The light has nothing to target, so the follicle is not affected. Blonde and red hair is treated poorly for the same reason. This is not a matter of finding a better clinic or a stronger setting.
Why
Laser hair removal works by selective absorption. The device emits light at a wavelength that melanin absorbs well. Melanin in the hair shaft takes up that light, converts it to heat, and the heat damages the follicle enough to stop it producing hair.
Remove the melanin and the whole chain breaks at the first step. A white hair has effectively no melanin, so it absorbs almost nothing. The energy passes it by. Grey hair is partially depigmented, which is why results on grey are unpredictable rather than absent: a few hairs may have enough pigment left to respond and most do not, so what you get is patchy.
Red hair carries a different pigment type that most lasers absorb poorly, and fine blonde hair has both low pigment and a small target. Both respond badly for related reasons.
Turning the power up does not help, because the problem is not the amount of energy delivered but where it goes. If the hair cannot absorb it, more energy simply means more energy available to be absorbed by the surrounding skin instead, which is how burns and pigment changes happen.
Why won't laser treat my light hairs?
Because there is not enough pigment in them for the light to be absorbed. This is the same reason a laser clinic may have offered to treat only your darker hairs, or declined to treat you at all. It was accurate advice about laser.
Will an IPL device work on my white or gray hairs?
No, for the same reason, and often less well than professional laser. At-home IPL uses broad-spectrum light and relies on the same pigment absorption. If professional laser cannot see your white hair, a home device certainly cannot. See do at-home IPL devices work.
Does electrolysis work on white hair?
Yes. Electrolysis puts a probe into the follicle and treats it directly, so hair colour plays no part in whether it works. A white hair is treated exactly the same way as a black one. The only practical difference is that white and fine hairs are harder to see, so lighting and magnification matter.
What the evidence says
The pigment-absorption mechanism behind laser hair removal is well established and is not a matter of dispute. Laser providers themselves publish skin and hair suitability guidance that reflects it. Electrolysis is recognised by the FDA as a permanent method that does not rely on pigment.
What to do next
If the hair you want gone is white, grey, blonde or very fine, stop shopping for a laser provider who can do it. That provider does not exist, and the ones offering to try are the ones to be most careful with, since treating unpigmented hair at high settings is where skin gets affected.
Electrolysis treats it normally. See gray, white and blonde hair removal, or electrolysis after laser hair removal if a course has already left this hair behind.