Nope, HS2 was cunningly designed to be completely separate from HS1 and the channel tunnel because why would anyone want to go to a place not london? If you are crazy and want to go to the mainland, you need to take HS2 to london, take the tube across town, and then go through customs and get onto the Eurostar.
Also there is apparently no point in designing them to connect because customs checks are physically impossible to do outside of london, which is why there are no international airports or ferry terminals that exist outside of London, and you definitely couldn’t do them on the train like anyone else.
Ohh value engineering, why do a job properly when you can do a much worse job for slightly cheaper and then get paid a lot more again to fix it.