The FAA will transfer any type ratings you have on your ICAO certificates, however, they will only put the ones that are required in the US. So any helicopter that weights 12,500 pounds or less will not transfer. Once you pass the ATP ride all the type ratings on your Private Pilot certificate will automatically transfer over. The ATP and type ratings use the same standards as published in the ATP Practical Test Standards.
You can do the ATP ride and the type raid at the same time. They are the same checkride. To confirm you will need to talk with whatever facility you are going to use.