Can a computer analyze audio quicker than real time playback?
Yes. Absolutely.
Algorithms can process data as fast as they can read them and get them through the CPU.
If data is on disk, for example, a modern NVMe can read at 5+ GB/s which is much faster than bit-rates normally used to store voice data. Of course, the actual algorithm being applied can be more or less complex, so we cannot guarantee it will be processed at the maximum read speed but there is nothing inherent that limits such analysis to be in real-time speed.
The same principle applies to video but that requires much more throughput due to the huge amount of data in such files. That obviously depends on resolution, frame-rate and complexity of the analysis. It is actually difficult to perform sophisticated video analysis in real-time because analysis is almost always done on decompressed video, so the processor must have time to decode and analyze in a short period of time and keep data flowing so that by the time some analysis is done, the next block of video is already decoded and in memory. This is something I worked on for almost a decade.
When you playback video faster, words are unclear to you but the data is exactly the same. The speed at which audio is being processed does not affect the ability of the algorithm to understand it. Software knows exactly how much time each audio sample represents.
I'd go a bit further than the current answer, and would like to contradict the idea that the computer is somehow "playing back" the files at all. That would imply that processing is necessarily a strictly sequential process, starting from the beginning of the file and working your way towards the end.
In reality, most audio processing algorithms will be somewhat sequential - after all, that's how sound files are meant to be interpreted when playing them for human consumption. But other methods are conceivable: For example, say you want to write a program that determines the average loudness of a sound file. You could go through the whole file and measure the loudness of each snippet; but it would also be a valid (although maybe less accurate) strategy to just sample some snippets at random and measure those. Note that now the file isn't "played back" at all; the algorithm is simply looking at some data points that it chose by itself, it is free to do so in any order it likes.
This means that talking about "playing back" the file isn't really the right term here at all - even when the processing does happen sequentially, the computer isn't "listening" to sounds, it is simply processing a dataset (audio files aren't really anything other than a list of recorded air pressure values over time). Maybe the better analogy isn't a human listening to the audio, but analyzing it by looking at the waveform of the audio file:
In this case, you aren't at all constrained by the actual time scale of the audio, but can look at whatever part of the waveform you want for however long you want to (and if you are a fast enough, you can indeed "read" the waveform in a shorter time than playing the original audio would take). Of course, if it's a very long waveform printout, you might still have to "walk" for a bit to reach the section you are interested in (or if you are a computer, seek to the right position on the hard drive). But the speed that you're walking or reading isn't intrinsically linked to the (imaginary) time labels on the x-axis, i.e. the audio's "real-time".
Your core question is this:
“Can a computer analyze audio quicker than real time playback?”
Other great answers here but here is — what I consider — to be a very commonplace real-world example of computers analyzing audio faster than real-time audio playback…
Converting an audio CD to MP3 files on a modern computer system is always faster than real-time playback of the audio on that CD.
It all depends on the speed of your system and hardware, but even 20-ish years ago converting a CD to MP3 files was always faster than real-time playback of the CD audio.
So, for example, how can a 45 minute audio CD can be converted to MP3 in less than 45 minute? How could that occur if the computer was constrained by audio playback limits? It’s all data on the data side, but constrained to human levels on playback.
Think about it: A computer is reading the raw audio data from a CD at a speed faster than normal audio playback and running an algorithm against it to convert the raw audio into a compressed audio data format.
And when it comes to transcribing text from audio, it’s a similar digital analysis process but with different output. A far more complex process than just transcoding audio from one format to another, but still it’s another digital analysis process.
PS: To the seemingly endless stream of commenters who want to point out that pre-1995 PCs could not encode MP3s faster than real time… Yes, I know… That is why I qualify what I posted by saying “…on a modern computer system…” as well as stating “…but even 20-ish years ago…” as well.
The first MP3 encoder came out on July 7, 1994 and the .mp3 extension was formally chosen on July 14, 1995. The point of this answer is to explain at a very high level that on modern PCs the act of analyzing audio quicker than real time playback already exists in a way we all use: The act of converting an audio CD to MP3 files.