We spent some time on this a couple of years back and yes, it's quite common for polymers of various kinds to autofluoresce pretty much across the entire visible spectrum, as long as you hit them with enough laser power. The emission peak is usually about 15nm higher than the wavelength of the excitation laser. If you have a "genuine" fluorophore with a proper resonance peak, like GFP, in your sample, it usually brightly outshines any of this unspecific polymer autofluroescence. But especially around the near-UV range (e.g. when imaging DAPI), it can interfere.

Some of the strongest autofluorescence we actually got from plastics commonly used for culture vessels...