Taking the advice provided in this thread, I reached out to the company that oversees our company's health plan with this exact question. Their response is as follows:

"Once processed, the change will be retro-actively effective back to the newborn's date of birth and any claims from the date of birth forward would be processed under the new plan."

Really happy with the response, and hopefully it'll actually work how she's saying it will. I appreciate everyone's feedback!