Absolutely not. My bands (platinum left, titanium right) come off as soon as I get home. I neither train nor race with them. I have a nasty scar from my original wedding band on my left ring finger where I came close to a degloving incident almost 20 years ago. Never again.
My wife also doesn’t wear her rings when training, either, for the same reasons (except she’s never gotten close to the same injury).
I have considered getting an infinity knot tattooed on my left ring finger, for when I’m training and racing, so I have something there.