Can the Arduino simultaneously implement 6 ADCs and pipe the data into a computer via USB?
The simple answer is no.
If you are talking about sampling the voltage from the pickup an an audio signal, you will struggle to do this with one pickup let alone 6.
If you sample the signal at say 20kHz to give a top harmonic of 10KHz then assuming 8 bit samples you have 20,000 bytes to transfer to the PC every second. Each byte takes 8 bits + 1 start + 1 stop = 10 bits so your serial baud rate needs to be 200K baud. The fasted baud rate (on the monitor) is 115K baud. You would also struggle to be able to receive that much data on the PC without occasional hickups. Assume you wanted to have a better sample size than 8 bits, then the next up would be 16 bits. I know the built in converter is only 12 bits but sending two bits per sample is perhaps easier than sending two samples in three bytes. This doubles the data rate you need to send.
Now multiply that by six and you will see it is a non starter.