"Freudig?!?" Is that even a German word? If it did exist, I think it would mean Freudian, not happy! (Have been speaking German for thirty years, in different regions, and I've NEVER heard this word!)
Yes, it is there. For example in a phrase like "In freudiger Erwartung Ihrer Antwort verbleibe ich" or something at the end of a letter. But I could see how you could get by for that long without having to use it. It sounds kinda old and formal. Froh is a lot more common.