A border fence would shift illegals to places without a fence, but that would still be harder than crossing at the current, easier unfenced crossings. A fence covering the entire border would help more, especially a double fence so that a ladder would not be enough to got through, and especially with daily checks for breaches and immediate maintenance that kept it from being worth the effort to tunnel/cut/whatever through.
Even a perfect fence would not be a perfect solution because a significant part of the problem is legal entry followed by simply refusing to leave. Still, perfect is not the goal. The goal is, or ought to be, making illegal entry much harder, followed by making the employment of illegal aliens much riskier. If illegals were fingerprinted, DNA swabbed, deported, and permanently denied legal entry, some would prefer to go home and apply for legal entry. If we enforced employment laws, employers would refuse to commit the crime of hiring illegals, and the illegals would have an incentive to go home. It's not perfect, but it would help reduce the problem to a manageable level.
The border needs armed men more than anything else, its the cheapest and most effective solution. Then we can debate the merits of a fence/wall/minefield later.