Yes. Some might have done so. Those with impeccable social standing could do so. Those with nothing to loose as well. Those with said social standing and the body to pull it off could make a great impression- some ladies (like Thérésia Tallien) at least. And there are those unfortunate fashion victims who inspired such mocking songs as this one...
Tune of La Bourbonnaise* would have a rather bad aftertaste for a contemporary audience, as it was used for rather mean songs only a couple of years earlier
Source "Journal des Dames et des Modes, Issue 61, Year 5" page 487 and 488
La Mode, ou la Sans-Gêne, chanson nouvelle sur un air ancien
Ancien air de la Bourbonnaise*
Grâce à la mode, Thanks to Fashion
On n'a plus d'cheveux bis. One doesn't have any hair**
Ah! qu'c'est commode, Ah! That's most convenient
On n'a plus d'cheveux, One doesn't have any hair
On dit qu'c'est mieux. One says, it's nicer***
Grace à la mode, Thanks to Fashion
On va sans façon, bis. One goes without putting on an air****
Ah! qu'c'est commode, Ah! That's most convenient
On va sans façon One goes without air
Et sans jupon. and without petticoat
Grace à la mode, Thanks to Fashion
On n'a plus d'fichu, bis. One doesn't wear a neckkerchief+ anymore
Ah! qu'c'est commode, Ah! That's most convenient
On n'a plus d'fichu, One doesn't wear a neckkerchief anymore
Tout est déchu. All++ is deteriorated
Grace à la mode, Thanks to Fashion
On n'a plus d'corset bis. One doesn't have a corset anymore
Ah! qu'c'est commode, Ah! That's most convenient
On n'a plus d'corset, One doesn't have a corset anymore
C'est plutôt fait. That's rather done.
Grace à la mode, Thanks to fashion
Un' chemise suffit, bis. A shirt suffices
Ah! qu'c'est commode, Ah! That's most convenient
Un' chemise suffit, A shirt suffices
C'est tout profit. It's all gain.
Grace à la mode Thanks to fashion
On n'a qu'un vêt'ment, bis. One has just one piece of clothing
Ah! qu'c'est commode, Ah! That's most convenient
On n'a qu'un vêtement One has just one piece of clothing
Qu'est transparent. What is transparent+++
Grace à la mode, Thanks to fashion
On n'a rien d'caché, bis. One didn't hide anything
Ah! qu'c'est commode, Ah! That's most convenient
On n'a rien d'caché, One didn't hide anything
J'en suis faché. I'm annoyed about this.++++
** probably referring to short hair styles
*** Not the singer/writer, but the ladies wearing short hair say it's nicer
****Without decorum, without air, grace, style, ceremony
+ Fichu or Neck-kerchief serves to cover a ladies neckline, what is widely cut by fashion, yet covered up by modesty
++ I assume the singer/writer means all = good behaviour, morals, modesty
+++ Muslin can be very sheer, it's a very thin and nearly transparent fabric
++++ Whether the singer/writer is annoyed about the fact that he sees everything and it might not always be pleasing to see everything (it's as today, not every hemline or shirt or bathing-suit suits everyone, then as today not all women can or ought to go without support) or whether he's annoyed that the element of surprise is gone, is left to our imagination.
I cross-referenced some words with a dictionary from 1836 as well as with my old 1932 dictionary, as sometimes meaning and scale of a meaning can change. (e.g. in modern French most people would understand "fichu" as "damned - lost" (Je suis fichu - I'm lost) - and the term "fichu" for neck-kerchief would only be used in reference to (traditional) costume.
If you are interested into old dictionaries, I recommend Google-Books - here an example from 1762
