No. The ability to move the fingers, wrists, and arms very rapidly. very accurately, and independently is very important indeed. But not strength.
According to a printout from an intro to Liszt's collected writings on technique, "Liszt paid much attention to the idea of strengthening the hands and arm in his practice".I'm sure it must play some part.
You do need strenght in the back, upper body and arms though...This is my main problem, because I suffer from muscle weakness it is often very hard for my arms to support my hands and wrists. When it comes to wrists and fingers it's more about flexibility than strength I guess.
I would think your bike riding would help some of that. While good cardio exercise it does require some muscle. Rowing would be good as well. These are functions that require overcoming resistance more so than lifting weights.
The only problem with that kind of exercises (including weight lifting) is that you need to do them with CLOSED hands, while for piano playing, you need exercises that OPEN the hand, not the gripper kind of thing.
The point of the matter is that all the hand/arm/finger strengthening you need can be done at the keyboard.
Yes. Try holding your hands out in a seven octave position, say, for two minutes. Easy? For you maybe, due to the body type your parents gave you, but not me. My body wants to eliminate those "useless" arm muscles and lay fat on my stomach instead. That is why I do the weight pilates program I detailed above. I also hold the five pound weight out from my body static for 30 seconds for each arm. If I don't keep up with this ( or anything else, rowing plus chinups might be fine) playing Pictures at an Exhibition or Lecuona's Maleguena is tiring. The exercises I picked can be done in an easy chair in front of the television, so boredom is not such a factor. Stretching is also important. I still do the army daily dozen "windmill" to stretch out the upper arms. I also do a hand stretch I learned in factory ergonomics training.
Piano sounds result from the speed of key attack, not from muscular force. And a good sound depends of relax of the wrists, arms and elbows.