The thing is that you are not using the core muscles that supports your back when you're cycling, so if your back aches when cycling, more cycling is not the answer.The back muscles will try to take up the slack and get more sore, whilst the core muscles becomes weaker.
Core training is not about becoming buff and building a 6 pack. It's about having a solid foundation, that will give you a base to train from and greatly help your recovery time. Yes, the first 2-4 weeks, it will have an impact on the amount of energy you got available for your regular training and if you ramp up the exercises as your core gets strong, you can still feel it, but the overall benefits far outweigh it.
The main problem I have with it, is that it's boring. It's gym work (never with heavy weights, but loads of lateral movements, with relatively light weights, variety of sit-ups, planks, etc) and that I've always found boring. (Which is why I only do it in the winter).
However, doing that for 2-3 months will benefit me for the rest of the year...