Serious question (ignoring the political perspective) will a wall reduce this or cause more injury by people trying to go under/over it?
Let's not belittle these people by pretending that they don't have access to the internet and world news. People will still come, but once word spreads that a wall in key locations is actually being built, at least some percentage of them will reconsider the decision and settle with aid from countries such as Mexico, which had already been granted to them.
Ironically, you might not need it since Trump and AMLO (the Mexican president) agreed for Mexico to stop the influx of migrants with its own resources. In a sense, we built the wall and are paying for it, by becoming the wall itself.