As an actual Chicagoan, I'll answer the OP's question: yes, I would. $25 is a bottle of wine, no big deal. For me. For a lot of people, it might be. Of course there's no guarantee that this fee would actually go to anything cycling related, any more than any other tax or fee---just look at all the supposed 'education' money the various state lotteries are supposed to generate.
But none of that matters because, as noted above, this idea (not even a proposal, much less a bill, much less an ordinance) is going nowhere. Mayor Emmanuel is not a fan and that is that. Say what you will about him, the man can count. As a commenter on the below article noted, even if all 16000+ estimated bike commuters were registered (forget about the kids and recreational cyclists), that's less than $500K, so wouldn't even cover the cost of implementation.
But by all means, A&S regulars, use this as a stepping stone to get up on your usual soapbox. It's cheaper than medication.
http://www.chicagotribune.com/news/p...,7405166.story
BTW: OP, in fact you didn't link the article originally. And Alderman Powell is female. The III doesn't mean the Pat Powell the Third, but the Third Ward.