I'm used a virtual ground IC to split 20VDC into +10V, -10V, and virtual ground. Would the Arduino be damaged if I connect gnd to virtual ground? and would this have an effect on its digital signals?
The answer to your question depends on the rest of the circuit. Please post a pic of it (hand drawn is fine).
A good general rule is to never apply a voltage greater than Arduino Vcc or less than 0 to any Arduino pin (relative to Arduino GND). The Vin or RAW pin is the only exception.
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I'd say "possibly risky".
Voltage is relative. For example, that's why you need 2 probes to measure voltage and it's why you need a "complete circuit". The voltage doesn't "exist" without a difference or reference. The ground inside your cell phone is a "virtual ground", "internal ground", or "isolated ground" with no connection to the outside world.
It depends on the other connections... If you know what you're doing you might be OK.
You could put 100V on the ground and 105V on the 5V pin and everything would be fine...
But if you were to touch the Arduino-ground and earth ground at the same time YOU are in danger and if you were to plug it into your computer's USB port you might blow the Arduino and the computer!
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No.
If that's the only wire connected, there's no voltage.
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