I posted an inquiry on this on a listserv and the answers have been interesting. Ohio says it may not be. Legal ethicists have intuitions both way on the topic. Some wonder if there isn't a generational divide on the question. Here's an article by Mark DuBois on the topic. Excerpts:
The Ohio Supreme Court just issued an ethics opinion (2013-2) on lawyers' use of texting technology as lawyer advertising. Seems some lawyers buy police reports about accidents and these contain the phone numbers of the parties. Some enterprising lawyer have tried to text the injured victims for business.
If texting to potential clients is something you think you want to do (or are already doing), get a copy of this opinion and study it. The court deserves props for figuring out this technology and how it fits into the traditional framework of lawyer-public communication.
I would have thought that sending a text message to the telephone of a person arrested for a crime or involved in an auto accident was a form of "personal, live telephone, or real-time electronic contact, including telemarketing contact" prohibited by Rule 7.3 of the Rules of Professional Conduct. The Ohio court likens it more to e-mail, which is permitted under Ohio rules, than to a chat room conversation, which is prohibited. However, it also cautions that there are some rules that need to be followed.
The text cannot create "real-time" interaction. I guess that means that the person cannot text you back. (I can imagine what some of those texts would say!) Or if the client texts you back, may be you cannot answer.
From the Ohio opinion: