This is a great question. As the other commenters have mentioned, to compare intensities across different wavelengths, an intensity calibration would need to be done because the webcam is not equally sensitive at all wavelengths of the visible spectrum. However, if you want to compare relative intensities at the same wavelength, then that is not necessary. If you want any sort of quantitative analyte concentration calculation, a sensitivity calibration would be necessary.
Since you said you are looking for qualitative results, I think you can indeed conduct your experiment without calibration, if you focus on comparing one wavelength at a time. One of the important things here is to make sure you have a blank or control so that you can observe the incident light versus the light coming through your sample. The Beer-Lambert law is generally reduced to A = ELC, where A is absorption, E is an empirical value for molar absorptivity, L is path length, and C is molar concentration. However, A = log(I-initial / I-sample), or the log of the ratio of the incident light intensity versus the light intensity through a sample at a given wavelength. The spectrometer can measure (in relative, non-quantitative terms) the light intensities that will allow you to calculate A, and thus calculate relative C. For your set-up, the path length L is the diameter of your sample bottle (since the incident light will shine through your sample vial before entering the spectrometer. It looks like you have the same size bottles for your control and your samples, so L won't be important unless you're looking for quantitative results (in which case you would need to know E too).