Just questions from a non-lawyer. Let's see who chimes in.
I say a resounding YES
I’m not a lawyer either, but you make a point. The Constitution was originally ratified with the promise that the Bill of Rights would be added. Originally there were 12 amendments—10 were ratified immediately, one in 1992 and the other is still out there.
The English have it much easier. Their Constitution is partially written, partially custom, but can be changed by Parliament whenever it wants to. Prohibitions against self-incrimination, double jeopardy, mentioned in the Magna Carta can be done away with.
I think the following speaks to your question rather well. It's an excerpt from THE LP'S FIRST PRIORITY by L. Neil Smith. The whole thing is worth reading. I know some folks on this site freak out at anything from a libertarian, but I think those folks miss things of common interest. This was originally written in 1994.
The first ten Amendments to the Constitution arose from a deal between the Federalists and the anti-Federalists; they were specifically required as a condition on ratification of the rest of the document by those who didn't want what civics textbooks call "a strong central government" but were willing to put up with it as long as certain limitations were imposed on its centrality and strength.
Those limitations were set forth in what we've come to call the Bill of Rights, but that's a misnomer, and a dangerous one. It should be called the "Bill of Limitations", because it doesn't apply to you, as I've said, or to me, it applies only to the State. As I've said, it's the Ten Commandments of American political behavior, a laundry-list of "Thou Shalt Nots", imposed upon the Federalist blueprint, that wouldn't make any sense at all, historically or logically, if it hadn't been intended -- by both sides -- to be absolutely binding.
No Second Amendment, no Bill of Rights.
No Bill of Rights, no Constitution.
No Constitution, no government.