No, migrants will just find other ways to cross the border, such as via boat or plane. Many if not most undocumented people are here having overstayed their work visas.
But will the volume be the same as an unguarded, unsecure border?
About a third, to a quarter, of illegals in the US today are ones that overstayed a visa. We can quibble on the exact number, but if you reduce the illegal entry rate by 50% that's a major reduction in the problem. What you are making is a continuum fallacy.
So, a wall alone won't solve the problem. Let's add that
all law enforcement can enforce immigration law to one extent or another. That is, any law enforcement agency can arrest someone for being here illegally. That doesn't have to mean some "Papers please" law, but rather we deny illegals access to legal identification while in the US. No driver's license, no ability to open a bank account, no ability to enter a contract, that sort of thing. No employer will hire you for fear of being arrested themselves. Toss in if you are here illegally and arrested, somebody will check your immigration status when necessary. If you're here illegally, no bail because you are a flight risk. You get held, get charged, get your day in court, and if found guilty, are deported.
The Yuma sector of the Southern border back in Clinton's term switched from catch and release to catch, hold, try, and deport. That is, you got caught coming across illegally, you went to jail, waited there until trial, if found guilty, you were deported. Within less than a month, crossings in the Yuma sector dropped by 90%. The word got out and people trying to enter illegally went to more 'friendly' border sectors where they wouldn't be held in jail if caught.
