Arthurian legend is a complex thing - it's a combination of different stories that were woven together over time and some added seemingly out of nowhere. This will probably end up being a bit rambling, sorry.

If you want some fairly heavy but interesting reading, I'd recommend The Arthur of the Welsh (eds Bromwich, Jarman & Roberts), although that's a much earlier version of Arthurian legend than le Morte d'Arthur.

In that book, Ceridwen Lloyd-Morgan says (p198):

French material could be regarded as extending and enriching the native stock of stories about given Arthurian characters, rather than contradicting an accepted canon.

Galahad was one such "extension". He doesn't appear at all until the 13th century, whereas the legend of Arthur had been around for at least a hundred years already, although some of them might go back to the tenth century. "The difficulty of dating the Arthurian poems is still as severe as Jackson described it in 1959." (ibid, Sims-Williams, p35)

Anyway, there are some references to (young) boys living in nunneries. From Medieval English Nunneries, Edited by G. G. Coulton (pp 262-263)

For Elstow, for instance, there is an early reference to a boy of five sent there for education by St Hugh, Bishop of Lincoln, towards the close of the twelfth century. In 1359 Bishop Gynewell prohibited[Pg 263] all boarders there, except girls under ten and boys under six.

The mention of boys in these references needs perhaps some further emphasis, for it is not usually recognised that the nunneries occasionally acted as dame-schools for very young boys. [...] But as a rule the boys in nunneries were very young; it was not considered decorous for them to stay with the nuns later than their ninth or tenth year;

So, it looks like there is precedent for young boys living in nunneries, but Galahad being there as a young man seems very unlikely.