Is the LED drop voltage difference between colors linked to the different wavelength energy?
The wavelength range of commercially available LEDs with single-element output power of at least 5 mW is 360 to 950 nm. Each wavelength range is made from a specific semiconductor material family, regardless of the manufacturer. Source: Photonics - Light-Emitting Diodes: A Primer.


The article is worth a read.



Figure 1. The LED color guide from Lumex gives a good overview of the various LED types, chemistry and wavelengths. For some explanation, if required, see LEDs and colour (mine).

Like all diodes (the D of LED), a certain voltage is required for the electrons to get them across the depletion region. The electron releases its energy as a photon. Your hunch is correct and the bandgap of the material gives the characteristic wavelength. Higher bandgaps give shorter wavelengths.



Figure 2. The forward voltage drops vary with current. What is an LED?.

This data for this graph was taken from various datasheets and carefully plotted. The LEDs, however, were from different manufacturers and there is some variation in the forward voltages. 

White LEDs, for example, are 450nm deep blue LEDs covered with wavelength converting phosphors. When a deep blue photon is absorbed by the phosphor it is reemitted at a longer wavelength (e.g. blue-cyan-green-red). So the white IV curve will be the same as the deep blue curve within the same product line.   I'm still working on this.