The president of the National Council on Teachers of Mathematics says no. While I agree with that, I'm not pleased with his analysis of the issue.
Algebra isn't the problem. I can't imagine that anyone truly believes that algebra isn't a "gateway" course--students have to be capable of more than just "doing" algebra, they have to know and understand algebra, and that includes both Algebra 1 and Algebra 2 topics. Additionally, Mr. Shaughnessy's fictional algebra track strikes me as exactly that, fictional.
I have no objections to different math tracks--probability, combinatorics, statistics, and/or data analysis. All are important, valuable fields that are certainly worthy of study, and are more directly applicable to non-math/engineering/science fields than is calculus. My fear, though, is that given the NCTM's history (which extends to this day) of favoring "interpretation of data" over computation, as well as their over-insistence on calculators and computers to do the computation, there's very little "math" left over in these so-called math classes. I assert that students must know how to do all the calculations themselves so that they can understand what the calculator or computer is telling them; they must have the "number sense" before they can truly interpret the data. In the same sense that students must know their multiplication tables before they use a calculator to do such work for them (do I really need to justify that??), so must students understand the calculations that the calculator or data analysis software will do for them. They should know both the calculations and the interpretation, but one before the other.
And I'll be honest here--I don't trust the NCTM when they as an organization say that they support computational ability as well as interpretation. Words are cheap, and the organization's actions of the past several years hasn't backed up those words.