This is definitely a controversial issue... I personally think it is okay for anyone to google anyone else, Ts included, but I know some people think quite differently. Whether it is unethical or unprofessional is a different question. I personally would encourage anyone interested in getting to know me to use google for gathering info that might not come up in direct interactions. I posted on PC before that I would be very surprised if Ts never google clients... some apparently don't, but I've heard enough of them saying they do. The public web is not private information really. What, I think, they should not do is tell the client (unless the client brings it up) - for me, that is intrusive and inappropriate.

One could ask similar questions about whether it's okay for a lawyer to google their client, or an employer to google job candidates. I am sure some people would argue a T is different, but IMO it's the same.