I was thinking that the GPIO was only referring to the Digital pins as well, but just like you, I can't say I am certain of that.
So your estimations put the Sampling Rate for the signals supplied to the Analog input is even less than 230 Hz? 7 ms puts it somewhere around 140 Hz, which is an unacceptable rate for what I intend to design (a guitar capable of being used as a MIDI controller).
I need to have a sampling rate of about 10 kHz at the very least. Plus I need to process 6 different signals (one for each string), so it appears that I am going to need to rethink my approach.
I definitely think that you are correct in that a Linux approach could remedy low sampling rate that is achieved with the Arduino IDE. The AD7298 ADC used on the Galileo is "spec-ed" as an 8-channel ADC with 12-bit depth, with a 1 MSPS throughput (according to the datasheet for the ADC, which I found a link to in the Galileo Datasheet PDF).
However, I don't have any knowledge or experience with programming as it pertains to the level of OS architecture. I have a fairly decent familiarity with C, and fundamental levels of Assembly Language and Machine Code (limitations of a typical electrical engineer here...), but I'm not really so sure I'll be able to handle things with Linux. The thought of that alone just scares me.