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Finding or not finding a person's marriage in county records would not be influenced by whether they were Quakers.... (if you're thinking that Quakers didn't register marriages, and this is what you're basing your idea that this indicated he was a Quaker, then don')...registering or not registering is no indication of any religious preference.... You need to have the following info to help decide why or not the marriage was included.
When was it mandatory for marriages to be recorded?...each state is different, so that's the first thing you need to find out. Before it was legally required, many registered their marriages anyhow, often at a local courthouse, but just as many didn't bother. So, you need to discover the dates for your state of interest, and how rigidly it was complied with. I suspect it you'll find that many counties did not issue formal marriage licenses until the mid-1800 or so, which is not uncommon in that timeframe.
I looked in Hinshaw's Quaker Encyc. and didn't come up with the name Pleasant Johnson/Johnstone in any southern meetings. The only ones I found were in Ohio, and were both men and women....so, be aware that the given name Pleasant was given to both sexes.