Not so much, according to a 4-3 decision from the Ohio Supreme Court:
“Coparenting” is not synonymous with an agreement by the biological parent to permanently relinquish sole custody in favor of shared legal parenting. “Coparenting” can have many different meanings and can refer to many different arrangements and degrees of permanency. The parties’ use of the term, together with other evidence, however, may indicate that the parties shared the same understanding of its meaning and may be considered by the trial court in weighing all the evidence.
The court in In re Mullin rejected a claim for shared parental custody despite written agreements. More on ConLawProfBlog, including opinion, here.