Hi allabouteva,
I personally have found immense benefits from strength training. During the winter months I do heavy strength training and during spring/summer I do "maintenance" work. Cycling or no cycling, it's actually a good thing to do when you are 30+ as you start to lose muscle mass. Strength training can also help to prevent osteoporosis.
I guess your question is will it make you a better cyclist? Most of the guys who ride may say no. But for a female, I personally think it will. Especially core exercises. Having a strong core will translate into power on the bike.
If you offroad, having a strong upper body can help a lot as well when climbing and even just absorbing the rough terrain.
If you tailor your strength training to be sport-specific vs just going in to do a few reps, then yes, I think it will help you become a better cyclist.
My 2 cents!
All limits are self imposed - Icarus