I would argue that the campaign against the European Constitution in France was not completely unlike the campaign for Brexit.

Opponents (on the left side of French politics) to the European Constitution argued that rejecting it would allow France to open negotiations for a more social leaning EU that didn't try to be only a giant free trade zone, but would also care about the well-being of its citizens (social net, minimum wage, etc.). We've seen where that went: there never was a Constitution B. No-one ever agreed to even try to write one. In short: just like for the Brexit, there never was any concrete plan behind the "no".

Ironically UK managed to duck out of most of the Lisbon treaty obligations (like the Charter of Fundamental Rights, judicial harmonisation and co-operation, etc.), while it would have been much harder -if not impossible- to do with the European Constitution... Had we (the French) voted "yes", we may have ended up with a Brexit 10 years before Brexit!

I’m just saying that the Brexit question was ultimately the same: too complex to comprehend, so people understood it in a ludicrously simplified form. It’s just less obvious when the complexity isn’t even known yet.

I think your conclusion is right. Having an agreement worked out first probably wouldn’t have changed much.