Photodiodes are normally operated in reverse-biased mode. So you connect a pullup or pulldown resistor in series with them and measure the voltage dropped across that. I can't see any problem with using an analogue multiplexer to read several of them from a single Arduino analog pin. However, the current passed by a photodiode is small, so the pullup/pulldown resistor needs quite a high value. So if you are reading the voltage drop directly into an Arduino pin, you need to take precautions to allow for that (i.e. add a delay between setting the internal and external multiplexers, and starting the conversion). Alternatively, use an op amp to buffer and perhaps amplify the signal.