The max ouput of the preamp its 2V
Is that peak or RMS? In any case, it's probably an approximation or a "worst case" spec (meaning that the preamp will clip at 2V or more), and it will depend on the power supply voltage to the preamp. Ideally, you could get 5V peak-to-peak (1.77V RMS) with a 5V power supply, but there will be a voltage drop across the output transistors and a real-world circuit will put-out less.
It's the same with a power amp specs.. If the spec says 100 Watts maximum, that means if you drive it to it's maximum, you should at least get 100W. You'd feel cheated if you could only get 90W, but you'd be happy if you get 110W.
Plus, it's an analog signal... Very unpredictable! The actual voltage will depend on how hard you pluck the string, the sensitivity of the guitar pickup, guitar's volume control setting, and the gain setting of the preamp.
You can get almost one volt out of a guitar pick-up, so the main purpose of the preamp is to present a high-impedance load that doesn't affect the guitar's output level or tone. The Arduino already has a very-high impedance input, but only for the positive half of the waveform, and you are not supposed to feed-in negative voltages.
If you don't care about the tone or sound quality while tuning, you might be able to skip the preamp. If you have a multimeter or access to an oscilloscope, you can check the guitar's output voltage. (A multimeter will be too slow to measure the peak, but you should get a good idea of the signal level.)
There are a couple of ways to deal with AC input. If you are analyzing the waveform with FFT to find the frequency, you need the whole waveform. The simple solution is to add a pair of equal-value resistors to bias the input at 2.5V (and a capacitor to block the DC bias from your preamp.. (That means that silence will read about 512 on the ADC, but that's easy to subtract-out in your sketch.)
If you only need to read the amplitude (maybe finding the zero-crossings to determine frequency) you can throw-away the negative half of the waveform. The easiest way to do that is with a series "current limiting" resistor (to prevent damage to the preamp) and a pair of "protection diodes" to prevent the signal into the Arduino going negative or going above 5V.
I'll leave it to you to research those solutions in detail.