Yes. The Separett Tiny and Villa urine-diverting toilets have been developed to have the fan running all the time. This not only keeps all odours out but also ensures that flies are not attracted to the toilet.
Having said that, we do have customers who turn the fan off overnight (using a timer switch) with generally no ill effects, although it must be stated that the manufacturer does not recommend this.
Turning the fan on and off can also shorten the service life of the fan.