Yes, and that's not completely daft. Intellectually the market liberalism seems to be made of very different stuff from authority, deference and tradition, so that intellectually the mix looks like a dog's breakfast. But in fact, of course, the transient element - trade - has to be undergirded by tradition (law, respect for property and so on). When you start to push the ideology hard, it all comes to bits, like when the free marketeers start saying liberalise the drugs trade. But a true conservative would understand that you should not think too hard about those things, because conservatism, according to its wisest proponents, is not an intellectual but an intuitive proposition. Neoliberalism had legs, but intellectually speaking it was the death of conservatism, by its constant thinking out of problems that were better left unsaid. The later Hayek is quite blunt on the anti-rational and traditional foundations of his philosophy (though insiders say the Fatal Conceit was really written by his editor W.W. Bartley), which seems surprising when you compare it to the pompously rationalistic critique of socialism.
Just to draw out another paradox, the free market people are right when they say Socialism owes much of its intellectual roots to Conservatism. English socialists were very close - Ruskin's Unto this Last was required reading for all, though it was feudalistic mumbo-jumbo. Marx and Engels were both keen readers of Carlyle (whose essay on Chartism sets out the essential argument of Marx's critique of liberal democracy before Marx does) - and of course their great inspiration in Germany, Hegel was reconciling liberal and conservative thought, with a philosophy that embraced both the liberal atomism, and the conservative wholism as different moments in the forward movement of Spirit.