Question from an outsider... does the NEC specify minimum distances between tubs or pools and electrical devices?
I know for sure that something like this wouldn't fly in any country using the distance tables from the European standards - they prohibit any devices or appliances except suitably wet rated water heaters within 60cm from the edge of the tub or (in case of showers without a shower pan) 120cm from the furthest reach of the handheld shower below 225cm above finished floor level. That doesn't mean average people couldn't touch the light/fan/whatever standing up in the tub with outstretched arms, but you certainly couldn't hit it accidentally.
I think Residential Building Code may prohibit this Fan installation even if the Tub wasn't there because of height requirements.
Bill