Wave Through and Inspection and Admission
A Wave through under current Board of Immigration Case Law is considered an admission so long as it conforms with procedural regularity. In order to be admitted legally to the United States, you need to be inspected and admitted by an immigration officer at a port of entry. Sometimes, officers will just look at individuals in a car and say go ahead. Yes, this is an inspection and admission so long as it was at a port of entry.
Proving a Wave Through
Herein lies the problem with this. How does a person prove that they were waved through. Affidavits of people that were with them at the time they entered can help. Normally the USCIS wants to see proof of admission such as a stamped passport along with an I-94 card. However, this is sometimes impossible with a "wave through." Most of the time USCIS will not adjudicate this type of application deny it and it will have to be litigated in front of an immigration judge.