Glad you think the theory might be OK.
I wasn't imagining that this would be perfectly precise or low-latency. Just that it might be an interesting, low-resource way to read up to 6 PWM channels at a time. It might be possible to increase accuracy at the expense of latency by stretching the sample over several PWM cycles - leaving more time for the Arduino to process.
(I'm also assuming that some kind of "switch on with the sticks centred" arrangement might be needed to let the Arduino measure neutral positions before we get started)
If the PWMs are parallel rather than serial, the values will make it into memory in parallel, then the Arduino's limited resources will churn through them in serial, resulting in latency. However, it might well be an acceptable amount. I don't have access to an RC set right now (mine's in long term storage 
no flying for me) so can't test, but it would seem that the key measure is "what fraction of the servo latency does this introduce" (or perhaps "what multiple of the servo latency..."). If it's a large multiple, this had better stick to slower moving applications.