Yes, the UV light from fluorescent lamps causes plastics to yellow, just like the UV light from sunlight. Of course, if you only turn on the light a few minutes a day (on average), then the effect will be limited.

If you want to avoid discoloration altogether (or at least the part due to UV light, there are still other factors: exposure to oxygen, heat, temperature fluctuations), but still want to reduce your energy bill, then I guess it's better to use LED-lighting.

Another alternative is to keep your toys behind glass covered with a UV-reflecting coating.