In reply to JimR:
Cycling in itself won't make you lose upper body strength, unless your caloric and protein intakes are to low in which case your body will look to scavenge nutrition from the muscle tissue you're not using (i.e. your arms). It also won't help your climbing, as you get heavy legs (muscle development) which are only really a hindrance on the wall. Unless your cardio fitness is abysmal, its very unlikely that this is the limitation to your climbing so you'll see little benfit in a climbing sense by improving the CV system via cycling.
The real issue is that time cycling is time spent not climbing. Unless you have 20-24 hours in a week to really commit to both, chances are your rise in cycling is coupled with a reduction in climbing. Why would your body maintain your upper body (at the cost of nutrients, energy etc) when you're not using it, and effcetively sending the message that you don't need as much muscle in your arms. The "use it or lose it" mantra outlined above. With regards to less endurance, I'm sure I saw something about localised mitochondira numbers and muscle use somewhere, if I could remember where I'd link to it. Effectively, the drop-off rate of mitochondiral numbers in your cells falls quite quickly if you're not putting that body part under enough load by training (obviously there is a base number when you're "untrained"). Again, the story here is use it or lose it - but it will come back quicker if you go from trained to untrained than if you were never trained in the first place.
The two sports are, in my mind, very compatible - when you're tired from climbing, your legs have plenty of gas and vice versa. A cycling day is a rest from climbing, and vice versa, to a degree - I'd still aim for one proper rest day a week. The only difficulty is getting enough volume in of each, due to time and motivation limitations.