Well, the problem with exiling them to the Wall is that the Night’s Watch only takes men, so you can’t really have whole families. But if you mean the Gift, yeah, you could resettle the Gift pretty easily.
Now, Ned already had plans for this, and Jon Snow has kind of put a whole bunch of wildlings there, although given the size of the Gift you can definitely fit more than 100,000 people there.
The biggest problem with this plan is that, other than the rural refugees, most poor people in King’s Landing aren’t farmers. They’re urban workers. Probably most of them work as unskilled, underemployed laborers – dockworkers, carters and porters, assistants to skilled laborers, petty vendors, lots of seasonal work, etc. So…how exactly are they going to feed themselves in the Gift?
Big problem with the whole “if you teach a man to…” nostrum is that people can starve to death while they’re learning.