Short answer: Yes, if the Fair Tax was passed, this would create an incentive for people to make purchases before the new tax went into effect. And, I might add, to defer income until after it went into effect. Like at my job we typically get a Christmas bonus on December 31 each year. If the Fair Tax was going into effect on January 1 and so the income tax also being eliminated as of that date, I think all the employees would be asking the boss to delay our Christmas bonus by a day or two to avoid the income tax.
As JoeTaxpayer says, houses are something of a special case as you don't just decide to buy a house, run out to the "house store", and pick one up. I think most people take months of looking at houses, negotiating with the seller, and going through all the paper work with the realtor and the bank.
Note that under the current Fair Tax proposal, purchase of an existing home, as opposed to a new home, is not taxed. The Fair Tax only taxes sale of new items, not resale of used items. There is no Fair Tax on used cars, yard sales, Goodwill, etc., and that includes houses. (I just checked fairtax.org on this point.) So for people buying an existing home, it would make no difference.
I WOULD certainly expect there would be a surge in sales of other big ticket items -- cars and televisions and furniture and the like -- in the couple of months before the new tax went into effect.
Any change in tax laws creates this kind of situation: incentives for people who will pay higher taxes under the new law to do something sooner, and for people who will pay lower taxes to do something later. A drastic tax change like this would create bigger issues than most tax law changes. One could argue that there should be some sort of transitional period where the old system is phased out and the new system is phased in. I think the people behind the Fair Tax are generally opposed to such a plan, though.
RE JoeTaxpayer's comment that there is zero chance of it passing ... It would be a dramatic change, and getting a dramatic change made is difficult. But big changes have been made in our laws in the past. Creating the income tax was a huge change, and yet it was done. Prohibition was passed and repealed, no reason why the income tax couldn't be passed and repealed. I don't see the impetus to get a law like this passed in the next few months or anything like that. But if, say, our next president was for it, the situation could change dramatically.