Is cycle sport encouraging uptake of cycling?

I'm not 100% about how the money makes it's way through but BC's reduced rates help juniors hugely with race entries, licenses and stuff.

We collaborate with a shop chain to get a crit series going for the yout' each summer. As a result we have a lot sprogs keen as hell and racing. This is all funded by our membership fees (less than £30 a year) and membership numbers have just risen and risen over the last couple of years and it's all good. We're now having to run 2 chaingangs and 'social' ride in the week and 4 rides at weekends (including one specially for kids once a month).

It's still really expensive to host a proper road race, but we manage. It's always a bit of a slog getting marshals.

If you ride a bike it makes no sense to me not to be in a club, even if it's initially just for the insurance.

Exactly. People forget (or are simply unaware) that countries with enviable cycling for transport 'infrastructure' (which we know really just means drivers not being cunts) also have an incredibly healthy club and race scene for all ages and abilities.
In Holland for instance, you find that prominent local businesses sponsor the local cycling clubs, in a similar way that Rabobank sponsors a pro team and national riders. There are more closed-road races in western Europe than most on here could conceive.