As I understand it, most, if not all genetic engineering uses a marker
gene to identify transformed bacteria. This marker gene was/is usually
an antibiotic resistance gene so the transformed bacteria will be the
only ones that can grow on an antibiotic laced culture medium
Most but color markers (which gives the host cell a color that can be used for selection) are also used. More complicated selectable-counter selectable markers are also used (ie HyTK gene). A counter selectable marker is a marker that kills a cells when it is present. A selectable-counter selectable marker is a hybrid marker that allows you to both select for cells with the marker using one selection agent and kill the same cell with a second selection agent.
So, every (most) GMO will contain a copy of a bacterial antibiotic
Well not quite. GMO ie Genetic modified organism, includes both prokaryotes (bacteria) and eukaryotes (plants, animals, and yeast). The promoters which drives gene activity in prokaryotes and eukaryotes are different. So a eukaryote markers do not work in prokaryotes and vise versa.
Furthermore, genetic modification of eukaryotes is difficult. Hence modified viruses are often used. These viruses are made in such a way that their genome has been replace by desired DNA playload. And as the payload size is limited, often time any unnecessary DNA is also removed, like prokaryotic markers which have no function in a eukaryotic host.
Lastly due to public pressure, there has been a push towards cleaning up after genetic engineering work in GMOs that are to be marketed to the public (GMO crops). So things such a selection markers are removed (either by use of counter selectable markers followed homologous recombination or site specific recombinases).
So, is it a fair question to ask if the unnatural proliferation of
antibiotic resistance genes in the wild due to the commercial
propagation of GMOs might be at least partially responsible for the
increase in multiply resistant organisms that we are seeing?
Given the wide spread use of antibiotic in animal husbandry and by the public general, and move toward removing selection markers in commercial GMOs, I do not think GMOs are the cause of the increase in MR bacteria.
A more likely cause would simply be because we are using so much antibiotics and thus there is a selection pressure to aquire multiple resistance. Remember all our antibiotics resistance genes and most of our antibiotics were acquired from nature.
Has anyone, for example, mashed up GMO matter, added non antibiotic
resistant bacteria, grown the mix up overnight, added the antibiotic
used as a marker in the GMO, incubated for a few days and then seen if
any bacteria survived?
Yes, lots of times around the world to varying degrees of sucess. I have personally spent time doing this and so have my labmates. It will work if you prepare good quality DNA that has not been degraded by endonucleases, the bacteria are very transformable (ie the bacteria has been treated to take up DNA easily), electroporation is use (to force the DNA into the cell) and you have prokaryotic marker. A eukaryotic marker, is a marker that works in an animal cells will not work in bacteria. So you have to engineer your GMO animal to carry both a eukaryotic and prokaryotic marker.