Can a laptop cooling pad eliminate (or largely substitute) the use of the internal fans?

The cooling pad would be likely to reduce the fan-spinning, but with no air circulating in the tight spaces of a laptop, you can't expect the fans to stay off very long--that Intel chip is generating lots of heat (depending on which one you have, up to 35 watts) and all that energy has to go somewhere. The fans push it out of the case. Conduction with the cooling pad can't cool any part of the laptop except the very bottom, because there isn't room for air to circulate naturally.

"First, I assume you're referring to a pad with built-in fans, in which case those fans are going to be making noise anyway.

Second, external fans are nowhere near as thermodynamically efficient as internal ones where a laptop is concerned. If your system is already hot, you're not going to see a 90/10 -> 10/90 reversal.

If you're talking about a purely heat-conduction-based cooling pad, then this is even more the case, although obviously the first issue won't apply."