At the annealing step of PCR it is the oligonucleotide primers that binds to the single stranded template and initiates extension. But do the two single strands also anneal among themselves?
They do anneal. Just at lower quantities as you have a molar excess of primers vs target. That is the reasons of having incomplete extension products deal to chimeras when you have two highly related genes coamplified in the same PCR (we deal with that issue a lot in 16S amplicons from environmental microbial communities).
Here is a good answer: https://answers.yahoo.com/question/index?qid=20100207230249AAKnTVp
And also, the annealing temperature used in the PCR depends on the primers (%GC and size), so it will be optimal for the anneal of the primers but not for the single DNA strands to do so - these are too big and therefore the conditions (including time) for them to anneal would be drastically different, I guess.
They do anneal. Just at lower quantities as you have a molar excess of primers vs target. That is the reasons of having incomplete extension products deal to chimeras when you have two highly related genes coamplified in the same PCR (we deal with that issue a lot in 16S amplicons from environmental microbial communities).