It was supposed to be a 5 gallon batch and there was so much foam when I dumped it into the fermenting bucket that I couldn't see there was only 4.5 gallons actually in the bucket. That's the only reason I was going to add the extra water.
At that point, when you were going into the fermenter would have been the best time to do it, before yeast pitch. It's common, even when brewing all grain and missing your post boil volume- it's called "topping off."
In fact if the "shortcoming" in your post boil volume was because you boiled away too much (which happens all the time, especially when people are starting out and haven't "dialed in" their process and realize that maybe they need to dial back their stove or burner during the boil because they're boiling too much away in during that time) then your gravity at that point would have been raised by EXACTLY the amount of points that at that point topping off to the 5 gallons would have brought the gravity back down to what the recipe said it would be.
It would have all balanced out.
Post yeast pitch, and especially post fermentation, I recommend brewers just go with and enjoy what they got. There's a lot of risks to messing around after, including the risk of oxydizing or infecting the beer they have.
one of the reasons we get the yeast into the wort ASAP is to get the yeast working before there's any chance of wild nasties which are competing for all that sugar to make 5 gallons of vinegar for example, after fermentation you don't really have that safety net.... Same with agitating the beer and even adding oxygen right water- yeast need oxygen pre-fermentation... oxygen after fermentation makes your beer taste like liquid cardboard.
It's best to correct things before you add your yeast- fermentation is really good for correcting things, and it really is the "point of no return" where you want to mess around.
After it is best to let it ride.