Power (watts) is part of cycling and strength is the main component of power. So by adding strength you should not be hurting your performance.
Also strengthening your core is very important for overall fitness not just cycling. If you have a strong core your legs have a platform to push against. Off-season is the perfect time to introduce your body to lifting weights since you are training less and is easier to adjust. I do strength exercises 2x a week now and I will keep doing some work as season starts. I record my experiences on my blog. You can take a look at these links:
Core Strength: http://www.thetallcyclist.com/?p=668
Weight Lifting: http://www.thetallcyclist.com/?p=681

Weight training is very important for balancing your body. With the correct periodization lifting during season is also possible, however, as previously mentioned if it takes you away from the bike it might not be as helpful.

Good luck with your training!