You're gonna need a public method on hacking the HOME architecture to send mons.
To my understanding, if it can be done, it'll be revolved around "mimicking/spoofing how HOME receives mons from a game", which would mean you'll likely need the keys from your Switch to emulate that process, which sounds like a risk if you ask me.
(Keys from your Switch = they're able to ban your Switch if they detect and block the method).
Even then, I have doubts that PKHeX will send into HOME for your. It'll likely be stated that "such a function will bloat the program", and you'll have to use the HOME spoofing program (if/when it exists) to send the PK8 to HOME.
In other words, as RoC said, "no".