You'll get opinions all over the place on this, and the data is somewhat mixed. To the extent there's much consensus it's something like this:
1) resistance training is good for your overall fitness, and helps with bone density which is important for cycling.
2) working on your core year round will help with fitness, likely helps your cycling to some degree, and has no real downside.
3) some light upperbody work helps fitness, and probably doesn't damage your cycling.
4) lifting for your legs, offseason, may possibly help some with cycling, although the data's limited other than for track sprinters, and won't hurt anythin as long as it doesn't take away from time on the bike.
Where it gets contentious is lifting for your legs in season. You can only do so much intensity work. To the extent intense lifting for your legs in season takes away from the amount of intensity work you can do on the bike, IMHO, it's counterproductive.
However, there are some people who lift for their legs all year, and do well on the bike. Additionally, there are some recent studies that indicate it can help performance on the bike.
__________________
You could fall off a cliff and die.
You could get lost and die.
You could hit a tree and die.
OR YOU COULD STAY HOME AND FALL OFF THE COUCH AND DIE.