There is some benefit to remove moisture from the air in your tires. Higher moisture content results in larger pressure increases as tire temperature increases.
Pure Nitrogen is dry. If you can somehow get dry air in your tires you get the same benefit.
It's not a big deal usually, but when your tires heat up from being used, the pressure of the tire increases. The more water vapor in your tires, the higher the pressure will rise as the tire heats up. Apparently this is a big deal for racing conditions. But I don't race with my TT.
My TT has a "nitro-filled tires" sticker on it. I've never put Nitrogen in them myself - just pump air in them. I guess you could try to air up your tires on days with low humidity.
Ed