According to the
Ohio Architects Board, a written agreement is required to engage the services of an Architect. All of the agreement's requirements are included in the above link.
There is no apparent e-mail clause in the regs. There has been an "e-signature" law in effect since the Clinton administration, however I do not know how that would help with a state regulatory board which chooses to deal only with written, hand-signed documents.
You should contact a lawyer familiar with Ohio case law in this area to be completely safe. A cursory Google Search returns this
Construction Attorney, as an example.