They have a diagram that emits a single gluon in the head of every particle physics article in Wikipedia. Is that a make-believe diagram? I couldn't expect that from them.
It is not a make-believe diagram. It is a completely valid diagram, but it i just part of something bigger. Also the two quarks in the diagram need to ultimately couple to something else. The "in" and "out" final states must be colorless.
QCD is a extremely complex theory, one usually computes a piece of the puzzle and tries to extract physical information from that.
Just to add to this: The part that comes this initial gluon emission (hadronization) is not very well understood since at this length scale the perturbative (i.e., feynman diagram) approach to QCD breaks down. See e.g. http://www.quantumdiaries.org/2010/12/11/when-feynman-diagra...