Yes, old units can perfectly survive within the metric system, as long as they are pegged to a standard unit like the gram or the meter. The point of the metric system (or any other legal system of weights and measures) is that scientific and commercial data and labels should be unambiguous within a certain polity, not that people cannot order a "pint" or a "demi" at the bar*.
* Un demi correspond a vingt-cinq centilitres de bierre, soit une demi-chopine (une mesure utilisée en France avant la Révolution et le systeme métrique).
Napoleon wrote against the idea of the metric system, with arguments that mirror some of the ones we read here ("good for scientist, but too complicated for the people"). Interestingly, one of the argument he raised was that the attempt by French revolutionaries to design a universal system -- not based on the traditional units of any country or on anthropomorphic measures like the foot or the coudée
but based on the properties of the natural world e.g. water fusion and boiling points or density -- was foolish because whatever the French do, the "national spirit of the English and German will prevent the universal adoption of the new system"... Two hundred years later, the Système international d'unités
(SI), inspired from the metric system, is used all over the world with very few exceptions.
So Napoleon was wrong: it DID pay off to design a purposefully universal system. Even the Brits have progressively warmed up to it and anglophone countries retaining the foot or the pound have come to define them in relation to the meter and the gram.