Um, not exactly. Where to begin? Museums are not the main source for buying stolen artifacts -- that "honor" goes to individual collectors (including, increasingly, collectors in the Gulf oil states with the wherewithal to compete against American, British, and Japanese super-rich). Museums make up only a small percentage of the buyers on the antiquities market worldwide. And most museums in the West have now already stopped buying illicit or even just dodgy antiquities. That is not going to put an end to collecting of illicit antiquities. Hawass is certainly correct to say that if museums stop buying illicit artifacts, the theft will be less, but by only a slight amount. No one believes that collectors will be much deterred by knowing they cannot donate or sell their antiquities to museums, when they can count on other collectors to buy their pieces should they need to part with them. And so long as a collector is willing to pop $57 million for a single "kosher" figurine, looters are going to try to find equivalent pieces and collectors will buy them even though they are not kosher.
So if Hawass really thinks that looting will be reduced to manageable levels by getting museums out of the market, he is badly mistaken. They have already gotten out of the market, and countries being looted continue to be unable to handle the problem with the resources they've got at their disposal. Countries suffering from antiquities looting are going to need more than just clean hands from the museum world: they are going to need money to pay for site guards, satellite monitoring, helicopters, etc. That money should come from the collectors and the dealers, and from the boards of museums as well.