Possibly. Adenosine 2',3'-cyclic monophosphate still does have an intramolecular phosphodiester bond, but this time the bond bridges the 2' and 3' hydroxyls, leaving a free 5' hydroxyl. Therefore, if the 5' OH were to have three phosphates placed onto it, it could theoretically be incorporated at the 3' end of a nucleic acid. The nucleic acid, however, could not continue beyond this point without breaking the cyclic phosphodiester bond in order to free up the 3' hydroxyl of the adenosine 2',3'-cyclic monophosphate.
Although this could happen in principle, this doesn't mean that this phenomenon actually occurs in natural mRNAs. Various factors (such as whether cells can make this compound and whether this nucleotide can fit into RNA polymerase's active site) could prevent the natural incorporation of this molecule into mRNA.