No.
My grandma did when I was little…I always made it to the toilet, as I thought puking in a bucket was gross. Puking, and feeling ill is bad enough. Using an ugly bucket has a way of making the entire situation feel even more disgusting, IMO.
It seems to me a lot of farm/midwestern families designate a bucket for this. I don’t know why. Lack of 2nd or 3rd bathrooms, I suppose.
My son used to cyclically vomit. For “the Pukes” I give him a large glass mixing bowl to keep on his lap, a pile of soft white towels near him and a damp wash cloth. When he was under 5, it was best to keep a bowl near by.
Now that he’s more self aware, he finds the bathtub to be much more comforting against his sore belly.
When I get ill enough to vomit, I’m usually found in the fetal position on the bathroom floor praying to vomit. When I’m not in the bathroom, I have always made it to the toilet from where ever I’ve been in the house.