No, LED wavelengths are a function of the chemistry used; you get one wavelength for each electron bandgap in the semiconductors used. You can get variations in relative intensity of the different wavelengths between batches due to varying mixtures of dopants, but the presence or lack of a particular wavelength is all down to the chosen dopants.
Originally Posted by mgb74
Different brands will have different selections of wavelengths (chosen from a handful of basic chemical options); if one LED from a brand has a bunch of parasitic emissions then all of them will. Likewise for a monochrome LED, all the LEDs of that design will be monochrome.
White LEDs are an exception as they are based on a phosphor excited by an UV LED, so they have a weirder spectrum that's much more subject to tweaking and variation.