False and correct.
If you'd use logic, Kage Bunshin only divide up Chãkra. When they're gone your Chãkra goes back normal.
If they use a jutsu that needs continuous Chãkra away giving, they won't be able to restore it back until done.
However, you are right in losing. Of course they can lose, but the Chãkra is replenished every time so.
If you are suggesting however, limited amount of Chãkra, I suggest you go back in the beginning of manga.
You obviously don't know the definition of unlimited, limitless, or any of the antonyms of limited. If they had unlimited chakra (which you clearly believe, since you said i need to re-read if i think it is limited) they could make an infinite number of clones, because every time they divide their chakra each one of them would have unlimited chakra, just like the original. Unlimited/2 equals unlimited. They could do this if they had unlimited chakra because their chakra would have NO LIMITS. Since they can't do this, this shows LIMITS to the AMOUNT of chakra they can hold at one time
With unlimited chakra, they could use jutsu after jutsu after jutsu after jutsu after jutsu after jutsu forever and it would never make a difference to their unlimited chakra pool. This isn't the case though. which shows LIMITS in the amount of chakra they can have at once.
Instead of unlimited, it would be more proper to say that they have a chakra source that can be regenerated quickly and through non-normal means (as in comparison to how an alive person regenerates chakra). However they are still limited by the amount and type of chakra they had during their lives, but their chakra pool can regenerate after or while a jutsu is being used depending on how much chakra was used in said jutsu. If something is draining chakra from an edo, they could potentially be left with no chakra (but they can't die because of edo). The potential to have no chakra does not by any means mean they have unlimited, as that is a clear restriction. Definitely not unlimited, since there are obvious and clear restrictions to their chakra.
Anyway you look at it, the edo's chakra is clearly restricted by limits.
Funny thing though, something I just noticed is that Minato says he is out of chakra and can't do that whilst he has the kyuubi's cloak on...