During HPLC-UV method development, specificity is checked on a lot of samples. If UV detection is performed at 280 nm, what would happen if there is a compound co-eluting exactly at the RT of the analyte but it has no absorbance at all at that waveleghth? Does it affect the signal of the analyte if it is in various concentrations? I thought that it might affect the signal as it affects light scatering/reflection and so on. Any comment is highly appreciated.

The spectrum of a compound can depend on the solution it finds itself in. If this hypothetical invisible peak was present in a large amount it could affect the spectra of the analyte. Unless this invisible peak is the sample solvent the effects are not likely to be something to worry about. You probably have seen the small jiggle that results from unretained sample solvent at the begining of a chromaotgram. Well, that helps calibrate the magnitude of the problem.