I was watching this documentary where people recreate a 13th century castle using period correct technology and tools and it got me wondering if there were ever accounts of castles being attacked while still under construction.
Yep, absolutely. The example that immediately jumps into my mind is Caernarvon Castle in Wales. Construction began in 1283-84 but it was attacked in 1294 by a Welsh uprising led by Madog ap Llywelyn. At the time it's believed the moat had been dug and the castle would have had walls approximately 12-24 feet high, as well as a few towers in various states of progress. The whole town (walled by this point) and castle would captured and burned. Of course we're talking about stone, so the damage wasn't complete and in 1295 the English recaptured the castle and continued construction. Unfortunately, the whole Welsh building program was too expensive and the castle was never actually completed.
As a counter-point - during the same rebellion the Welsh attacked Conwy Castle located nearby. Conwy had been completed ca. 1287 and was able to repel attack with approximately 40-50 men garrisoned which shows how vulnerable these structures were in an unfinished state.
Sources: Taylor, A.J. Caernarvon Castle and Ashbee, J. Conwy Castle (both published by CADW)