Variable-contrast papers, and their filters, are all designed for tungsten (3200K) light. As provided by condenser-head enlargers with incandescent bulbs, or dichroic color heads.
I use a stabilized cold-light head, which provides a blue light meant for graded papers. Not ideal- but I've successfully printed on modern VC papers for many years. Certainly contrast grade spacing is not consistent, and high-contrast negatives can be difficult, but I've almost always been able to make a good print. In the past I used a CP40Y filter above the negative, but eventually decided that it wasn't necessary.
The yellow-green light from the fluorescent Omegalite will certainly cause contrast-grade issues with VC papers. Problems like slow lamp start-up/shutdown, and brightness increasing with temperature, might be larger problems. But testing will give you your answers- just be ready to use a lot off paper finding out.