The other thing to deal with is that typically the LED array is driven from an LED driver chip (and you just upload ASCII data to it, via e.g. SPI) and you have to sample the lines to see when it is scanning the display. And is is probably scanning nonstop, so there is no obvious point for you to jump in and use an LED segment to measure the ambient light. One might have to blank the display (usually there is an explicit function, as well as a brightness control one) for a brief time. However if you disconnect the one segment, the other scanning won't matter...
A PIN diode does produce little current from ambient light, but I've done it. Historically people used LDRs which give you tons of "output", as well as having a very slow response which can be handy.
But another consideration is that the light sensor will be picking up some of the display light, so you want to read the sensor only during display blanking. That is why I used a PIN diode; it's very fast.