For a blind signature scheme you require the blindness and the unforgeability properties to hold to call it secure. For your question the latter is of interest.
Unforgeability here essentially says that if an adversary queries signatures for $n$ messages $m_1,\ldots,m_n$, then the adversary must not be able to efficiently compute another valid signature for $m^*$ such that $m^*\neq m_i$ for $1\leq i\leq n$ (essentially a one-more forgery).
If your second point would be true, then the adversary would query for some message $m$ and the forgery would be the blinded message and would be trivially accepted, since it is accepted by the verification algorithm.
Consequently, you do not want to have ii) in the standard definition of a blind signature scheme.
The question is: why would you require ii) to hold?