No.
Normally you ask a web service with some key words to compute the AI answer. So the web service needs the compute power, not your own system.
This counts for both cases: pre-generated dialogues as well as realtime generated. (For the latter you need an active internet connection additionally of course.)
Technically you CAN run an AI-system also at your home computer. Some engines are pretty small. But this would indeed expand the system requirements...
Real time interactions requiring an internet connection is much less than ideal. For some consoles like the switch, internet access in games requires a paid subscription. And you can't run the AI on the switch because the switch is an old console that struggles to run top end games sometimes, so expanding system requirements is out of the question. This means any implementation would not be able to be used on the Switch.
Ultimately I feel that while AI is interesting, it creates far to many problems. What if a character said something hateful or racist? With real time AI, you will not be able to garentee these instances will not occur, which is even more of a problem as many of the players of SDV are kids.You could solve this by pregenerating and approving dialogue, but you still have to vet, edit, and implement said dialogue, so it still takes up a lot of time and at that point it would be better to just write more dialogue that is good and fits the character.
I know I wrote a lot, so in summary: good as a mod, should not be implemented into the actual game.