We like the mugs as a souvenir, so we purchase them anyway, but no, you really don't need them with CL.
We stayed at AKL CL and they have cans of soda and cartons of milk, but everything else is from a larger bottle or pitcher such as water, juice, etc.
They do have to go cups for coffee, tea, hot chocolate, etc.
We brought back several cans of soda each time we went to the lounge to put in our room refrig. for after the parks close, as the CL pretty much shuts down at late night. (different than I was used to at Poly.)
I think they stopped bottled water quite a while ago since too many of them were taken for the parks, etc.
I did see people filling up empty water bottles with the water there for the parks. I thought this was a little border line!
Enjoy!