That's only part of the story...
Perhaps the main reason why high-pressure Xenon gas is added to incandescent bulbs is so that the Tungsten filament can be driven harder (to a higher temperature) and therefore produce whiter, more brilliant light.
What the Xenon gas does is physically reduce the ability of the Tungsten to vaporise from the filament and migrate to the inside face of the bulb envelope where it can deposit because it is comparatively at least, cooler.
Xenon gas at high pressure does this better and more effectively than the likes of Krypton gas.
Still, over time in use (especially since the bulb is heating up and cooling down a lot) the inside of the bulb will darken with deposits from the filament.
Some companies add some Halogen gas to the mix that combines with the vaporised Tungsten before it can reach the wall of the bulb. Instead the compound returns it to the filament where the intense heat breaks it down and the Tungsten is redeposited back onto the filament. Unfortunately not in the same place it came from so eventually the filament will become thin at one or more points and more likely to break if subjected to shock etc.
Bottom-line: Yes, Xenon bulbs will loose brightness although this will take longer compared to Krypton bulbs all things being more or less equal.
Al