If I play Celia Mae – Friendly Receptionist and I don’t have any ready ink to use her Please Hold ability, do I still have a character that can’t quest or challenge?
No. If you can’t pay the ability’s ink cost or choose not to pay it, it’s the same as if you choose “no” for the “may” part of the effect. This means that no part of that effect happens, so there’s no character chosen.
Official set release notes — Attack of the Vine!