No coincidence, you must work in an ICU before CRNA, every school requires at least 1 year as an ICU RN. Usually adult ICU's are preferred over the Peds ICU's but not always. As an ICU RN you will become proficient and familiar with a lot of the equipment you'll be using as a CRNA, such as central lines, arterial lines, Swanz, vasoactive infusions analgesics, sedatives, paralytics, ECG interpretation, etc.
You'll also need to work on getting and keeping your CPR, ACLS and PALS certifications up to date. Other people have numerous other certs, such as CCRN and TNCC. You'll also need to take the GRE, almost all CRNA schools require it though some will also accept the GMAT I think it is. Though not all schools require CCRN the questions asked during you interview alot of times come from this material.
All CRNA programs require a BS degree, I think a BSN is probably preferred but alot of schools will accept other science based BS degrees. I pretty much took the road you're looking at. After my ADN program I went right to an ICU at a Level 1 Trauma Center (Burn ICU, specifically) while working I did a RN-to-BSN program and took the GRE....twice, (I already had CPR, ACLS and PALS because I was a Paramedic prior to my ADN program) I didn't get CCRN but I studied the material. During my interview I didn't have any technical questions but we had to take a written test. Some schools however ask technical questions during the interview.
Hope some of this helps, if you have any other questions...fire away.