Such a bill would be some strange combination of repeal and revenue bill as well as well as more likely that not a spending bill since elements of "transition" would be thrown in also.
It would be a catastrophic failure in accomplishing the purpose you claim for it.
Much better would be to pass the FairTax as presently constituted eliminating the IRS and its appurtenances and then (or concurrently) have a cleaner separate repeal bill (either with or without the provision to make income taxation unconstitutional). In this way, such an amendment would stand an excellent chance of passing Congress and being sufficiently ratified to make the amendment effective all the while providing an operational (and quite effective) system of taxation.
Done this way, the passage of the FairTax not only provides some protection against any short term (7 year) attempts to re-institute an income tax, but it also makes the repeal of the income tax easier since it would now be an anachronism much like the Prohibition amendment - which you'll note did not make it unconstitutional to prohibit alcohol again ... but it's certainly not likely to happen in our lifetimes.
It would be the same way with the FairTax and the income tax; once gone the citizens will have no desire to return to it and that will be amply clear to the politicians since with enough votes to pass the FairTax into law, there will certainly be enough to defeat any reinstatement of income taxes. But if banned by constitutional amendment, that's even better provided its done the reasonable way.
That is another big plus for doing it this way, rather than you fooling people that it will be accomplished later. Because it is very difficult to get an amendment to the Constitution ratified. Much more difficult than passing a tax bill.
You are merely making excuses because you know that a new Constitutional amendment isn't going to happen. Three-quarters is a lot of states...38 to be exact. And most states have income taxes of their own to contend with.
I'll guarantee both of those right now.