That wouldn't seem to make much sense on a practical or theoretical basis. Clause 18 says "the foregoing powers" which would seem to mean the previous 17 clauses, including the first one. I don't understand how "The Congress shall have Power To lay and collect Taxes, Duties, Imposts and Excises, to pay the Debts and provide for the common Defence and general Welfare of the United States;" can be construed as anything but a "power," and therefore covered by Clause 18.
I didn't say that about Clause 18. My point is that Clause 1 doesn't grant Congress the power to provide for the common defense and general welfare; it says that Congress has the power to levy taxes to provide for CD & GW - that is, to levy taxes in order to provide for CD & GW. As phrased, that is a limitation on the power of taxation. It's basically saying that Congress can levy taxes for revenue purposes only. The actual powers to make use of that money are granted elsewhere in the document, under specific clauses granting specific powers. And as others on this thread have pointed out, that's exactly how James Madison (and many others at the time) understood that language.