Determining the reaction order of acetylsalicylic acid to salicylic acid with a spectrophotometer
I think your reasoning is sound. However, a factor you may need to take into account is that you have a number of possible related species here, each of which has a different UV absorbance spectrum. You have acetylsalicylic acid, acetylsalicylate anion, salicylic acid, salicylate anion, and salicylate dianion (this one will probably have a markedly different UV spectrum from the others). The relative amounts of these species present would be affected by pH, so it would be important to buffer the reaction solution, to maintain constant pH.