Not if they make the illegals build it. When they're picked up, make them work on the wall to cover fines for entering the country illegally, to make restitution for tax-payer funded services they obtained this country and to earn their tickets home.
After working on the wall they need to be fingerprinted, photographed, eye scanned & DNA sampled for future crimes.
Many come in and out of the US many times, that makes them
multiple law breakers. We know they break many others as well and this would give a data base to prove they had done it before.