Well, I am looking to find a peak in the signal that happens in 0.00005s, would I be able to find it with the built-in ADC? I also need to measure the time when that peak happened. Is there a way I can read it at 44.1kHz until a threshold is reached?
You've got your answer, so you know you'll need different hardware to read that fast, or to read the highest frequencies.
But, to get the practical "peak" or "loudness" of real-world sound you don't need to read that fast and you don't need the highest frequencies.
Sound is dominated by lower/mid frequencies... If you want to get a "feel" for that., load a music file into [u]Audacity[/u] and apply a high-pass filter at 5kHz. You'll hear how quiet it is and you'll see the same thing on the meters and in the waveform display. Then try the opposite experiment with a 5kHz low-pass filter. The peaks/loudness won't change noticeably. It will just sound a little "dull" or a little "lower quality". In fact the measured peaks may be higher when you filter-out the highest frequencies, due to the "side effects" of filtering.
Depending on your application, you might also consider using a [u]Peak Detector[/u]. The peak detector quickly charges a capacitor to the peak and then it slowly discharges (typically over several milliseconds or more) giving you plenty of time to read the peak and potentially freeing-up the microprocessor to do other things between reads.
There are real-world limitations to how-fast a peak detector can work (depending on the components) so you may have to experiment to see if it's fast enough for you.