I caulk around all tubs, showers, toilets, and vanities in bathrooms that I remod.
Especially around toilets. If they leak, it keeps the water contained to the toilet area.
I always seal the bottom of vanities or any wooden structure that meets the floor with polyurethane (3 coats for assurance.)
I forgot to mention when I caulk around toilets I don't caulk in the back (about 2 inches). If the wax ring starts to leak it gives the water a place to go and hopefully it is easier to detect. If you totally seal it especially a second floor toilet, you won't know it is leaking until it stains the ceiling below. Just my 2 cents worth.
Anyone who has ever picked up a commode that has been sealed and later leaked knows what they are talking about. The stench will permeate the house and MAY go away in a day or two. Here, we get these little, nematode looking things that want to slither all over the place.
I would definitely not recommend sealing the entire base.