Extrapolating on the expected hardware, it's likely going to be either inaccurate, have very high latency, or both.
Even Mycroft which open sourced everything else still runs the voice recognition part in the cloud because it's not possible to host it locally without rather beefy hardware that the average user won't have around (and even that has high latency). I did try some offline speech to text alternatives for it but they all more or less sucked to be frank.
Another option, if you are a bit more open with "sharing" data and you don't want to miss out the best TTS, is enabling google or azure cloud services - with the big difference, Alice will only send the sound right after detecting your hotword (only while flashing her LED and asking you "yes?" before the recording starts). Nothing else would be shared.
That's the main gripe I had with Mycroft, as there was no going around this:
"Hey Mycroft."
long pause
"What's gonna be the weather at 11 tomorrow?"
even longer pause
<answer>
Which is frankly so unnatural and just too annoying to be practical. And it feels like something that should be very straightforward to implement in terms of logic.
Another thing to keep in mind is, we use intermediate results for the ASR. Means already while you are speaking, the input is parsed. Only a few ms after you go silent, the parsing is finalized and NLU/TTS will start right away.
Of course with a bit bias, I'd say it is more like: "Hey Alice" "Yes?.." "What's gonna be the weather at 11 tomorrow?" short pause (.2 seconds?) <answer>
I mean, would it really consume that much extra power to just have a second sink that's just a N-second circular buffer, so you got the samples after the wakeword ready for speech recognition when the wakeword is detected?
I think the ballpark figures for the Pi 4 are 0.5 A when doing nothing, 1A when doing something intensive a single core and 1.2A when at full multicore load.
edit: Nope Vosk is doing much better than I expected. Thanks a lot for the recommendation!