Obviously a little fluoride will be ingested. However it is doubtful that this would increase much the total amount of fluoride that is ingested daily, mainly from the plants that you eat and from the natural water that you drink.
When you brush your teeth with fluoridated paste or you wash your mouth with a fluoride solution and you spit it, most of the fluoride acts against the tooth enamel to harden it and only a little is ingested.
On the other hand, when you drink fluoridated water, only very little of the fluoride acts against the tooth enamel to harden it and most of it is ingested, which will provide no further benefits, but which might have bad effects.
How there is even a discussion about which choice is better, beats me.