Nope... All you need for support is the 2x4.
This is stick framing/platform construction.
If you had a post and beam home this would be a concern.
This is typical stuff like I said, your doing fine.
No need for PT unless it is exposed to the weather or against concrete.Like the sill plate you will replace at the bottom.
Dont forget to also re-insulate before you close it up.
Then paint all cuts and sides on your trimm and exposed siding before you install it.