Are there any examples in nature of two polypeptides joining into a single, continuous, third polypeptide?
I am not aware of anything precisely corresponding to your diagram, but the somewhat related behaviour of inteins may be of interest in this respect. They are defined in Wikipedia as:


  An intein is a segment of a protein that is able to excise itself and join the remaining portions (the exteins) with a peptide bond in a process termed protein splicing.


So, unlike either ribosomal or non-ribosomal polypeptide (e.g. antibiotic) sythesis, they catalyse a peptide bond between peptides rather than an amino acid and a peptide. However these are already part of single polypeptide chain before the intein itself is spliced out.

 

[Modified from Intein_mech.png to fit page. — The mechanism of protein splicing involving inteins. In this scheme, the N-extein is shown in red, the intein in black, and the C-extein in blue. X represents either an oxygen or sulfur atom.]