Yes, I mostly agree. But they were constitutional monarchists, not absolutists. And usually their fascination for Bonaparte ended when he actually took power. They wanted something like Elizabeth II, not Louis XIV.
They were liberal in the sense that they supported individual freedoms, and they called themselves liberals. It makes no sense to call them otherwise. They were on the left because the original left-right divide was about individual rights, not socialism. Though the Overton window moved fast and radicals one day often ended up moderates the next week without having changed their ideas.
But they were not conservatives at all; even though their constitution kept a king, it had pretty much nothing to do with how the ancien régime worked. Nowadays they would be centre-right more or less like the UK’s Liberal Democrats or the French centrist parties.
What’s interesting is that the American use of “liberal” to mean “radical” is at odds with the historical meaning of the word, and how it is used in some other languages. That’s why some people are confused with neo-liberalism being a right-wing ideology.