Does conjugation support gene selection?
Interesting Question (glad the "group selection" post got you thinking!)

Me and two friends thought about your question during our Biology BSc at ICL (in fact we also thought about an even more puzzling phenomenon called "bacterial transformation" which is like conjugation, but they incorporate genes from dead bacteria!!) our first year course convener recognized our answers as "most likely candidates" so here they are:

1. Stress-induced Experimentation Hypothesis 

The likelihood of conjugation/transformation occurring may change for a bacterial population as a whole depending on how stressed it is (or perhaps how unfamiliar the environment is?). Stress signals could cause the population to be more "risky" and take up the DNA from surrounding living/dead bacteria and incorporate it with its own genome: "the hell, we're out of options.. lets transform into something that resembles the indigenous species of this strange ecosystem!". Indeed Bacteria have memory (see: chemotaxis) this means that perhaps they can be able to tell whether they have been receiving more stress now as opposed to before, meaning they can "trial and error" with various genes that have been imported within their plasmids! — "Let's try this gene, oh wait... I'm dying, hmm let's kill off this plasmid and take some more genes!".

In reply to this my course convener said: 


  "ah yes, a switch from asexual to sexual reproduction occurs in
  many organisms under stress. The genes that cause the
  sex/transformation to occur may gain a net benefit from recombination
  with genes taken from other organisms/the environment."


2. Diversity Plagarism Hypothesis 

If we look at the entire population of conjugating bacteria as a single competitive unit itself (e.g. like a tissue is a coordinated group of specialized cells) that can compete with other populations of bacteria who cannot conjugate the conjugating population will "win". This is because a conjugating population will always have much higher phenotypical diversity as it can mix traits between the individuals. This means a conjugating population is much more efficient at undergoing natural selection for beneficial traits or trait combinations. 

Think of natural selection (coupled with mutation) as an inventor... something that helps you invent much "fitter bacteria" is the ability to pull things apart from this bacterium and that bacterium and glue them together, this is essentially what conjugation/transformation does!! it allows you to pull bits from this bacterium and stick it to bits from that bacterium to get a "super-bacterium". It's like open source technology (free to share) as opposed to patented technology!! Conjugation is immediately a good thing because it means you can "steal" cool technology from living/dead bacteria and incorporate it into your population's gene pool!

Hope this was helpful!