Is it healthy for no frost fridge to have water in ice cube forms?
In short, it's within design tolerance.
Frost-free freezers work by generating a periodic warm-up phase which lets any ice melt. The water is then drained to near the heat exchanger, which will then evaporate it off outside the freezer body.
Ice cube trays don't generate sufficient additional water vapour within the freezer compartment to compromise this process - except in the runners directly surrounding the trays themselves, which for some bizarre reason don't seem to ever stay as frost-free as the rest of the compartment;)