it doesnt gather chakra, it gathers natural energy. It is then up to the user to combine that with his/her physical energy(aka stamina) and spiritual energy to form what is known as sage chakra(a stronger chakra).
btw normal chakra is made of just physcial + spiritual energies.
This is how toad sage mode works anyway
I dont know for sure snake/dragon sage mode works the same way. Main reason for this is that snake/dragon mode users seem to jump straight away into their sage form and seem to be able to say in that mode for a very long time. wil have to wait and see.
Oh by the way itachi fans out there, itachi respected jiraiya because he knew sage mode isnt a joke, just how itachi prasied kabuto's strength in his dragon sage mode. see everything makes sense if u let it.