It's possible. But please note that I don't exactly go to "work" in my own office where I would have the liberty of changing shirts at will; I visit clients and usually go there for a specific meeting.

Maybe I could arrive early and change in the men's room, but that would still be a big hassle. And when I visit two or more clients in the same day, how many shirts would I end up carrying? And who's ironing these? (If you must know, I iron my own shirts, and like to make them last more than a day whenever possible...)

I said in another post that I never met anyone at my clients' offices who commuted by bicycle, but actually I did; last year I met a man who lived in Nanterre and worked in the center of Paris. So he took a bike in the morning, going downhill, and went back home in the evening using the subway.

This only works because there are special trucks that take back Velibs uphill every night; he couldn't do that with his own bike. The Velib trucks didn't exist when there wasn't any Velib, so it's unclear if this guy's behavior actually saves a lot of fossil energy or just a little.