RaygunGothic,
in theory yes. The interesting part is how precise do you want that measure to be and if the PWM signals on all line are staggered or come at the same time.
For the precision, if you want to discriminate between 1024 positions, you need the measurement to be precise to the µs. That's 16 clock cycles on a 16 MHz cpu.
If your PWM signals are generated by an old style receiver in a serial manner, you plan probably will work. But it seems newer receivers start the PWM for all servo at the same time. With those, you might get two signals ending roughly at the same time and the processing of the second will be delayed while the first still runs thus affecting the measured time for the second.
As I wrote earlier, if you have a system that reacts slowly to controls like a steam boat or - I imagine - a blimp, you also might get away not reading every single PWM signal but cycle through the pins and concentrating on just one at the time. This might not work for very twitchy application where small delays produce big consequences.
Korman