Sure, pick and place at $200 is possible, but only if those $200 are used to pay somebody else to assemble the boards.
Otherwise, with $200 in parts is hard to build even a decent 3D printer.
It reminds me of this one:
http://hackaday.com/2014/06/04/thp-entry-a-300-pick-place-3d-printer/At $200, maybe something that moves and buzz can be built, nothing more.
For sure, not a usable pick and place machine.
OpenCV is not magic. A single frame can take seconds to process, and this happens at very low resolutions. At high resolution, it can easily go to minutes. Not all parts with the same part number are visually identical. Don't count on recognizing the parts visually. Since a human can hardly do that under a microscope, a machine vision will never do it reliable. In theory, it's easy, in practice, it will just not work.
This is not a one man weekend job.
Sure, we can talk about it and come up with crazy ideas, but that's pretty much all it can be done at $200.