No effect whatsoever. We're talking about inserting an extra maybe 20-50 DNA bases into a genome of a billion or so bases. Would be totally undetectable unless assayed using specialized molecular diagnostics methods.
Also, the DNA added would be chemically indistinguishable from the As,Ts,Cs and Gs already in the genome, so really the chemical characteristics of the plant would remain essentially unchanged except they'd now contain the short barcode sequences that would "look" like regular DNA in every regard except their specific sequence, which would be unique to the engineered strain and therefore trackable. @dbroze