Question: is it possible to disable the beep feature on the S1 when the network connection fails?
Apparently,
no.
On the S3 there's limited control over the beeps, on the S1 it's apparently not present.
Presumably if you messed with the control board's firmware code, you could disable it.
If you don't mind (mostly) doing away with beeps altogether, try taping off the buzzer (it's the black cylindrical bit with a hole in the middle at the corner of the board), or desoldering it completely (can try sticking an LED across its pads if you want to keep some form of feedback).