Public Key Encryption scheme with small messages among many parties
No, if you publish an N bit message it can hold at most N bits of information.

An N-bit accumulator value doesn't magically hold more than N bits of information in the same way a hash value does not hold the string it is calculated from. Verifying accumulator membership of a given element X requires storing a witness value for that X (essentially CurrentValue - X). Membership is tested by checking if witness + X = CurrentValue. Accumulators work only because computing a witness value for an arbitrary X is a hard problem, though such a value is guaranteed to exist.