Welcome to allnurses!
There are a number of existing threads on this site about CNLs programs and roles -- you could find them by using the "search" button, if you wanted to review what's already been discussed.
A CNL degree will not, by itself, allow you to go into nurse anethesia; you would have to return to school and complete a CRNA grad program (they require a minimum of 1 year experience working as an RN in critical care, among other things, and are extremely competitive).
I, personally, have only seen one job advertisement (literally, one
) for a CNL in my area to date (and I follow all the nursing listings regularly). There's not a lot of evidence out there that the CNL role is catching on in hospitals (other than those affiliated with universities that offer CNL degrees ...
However, a CNL degree (and licensure) would prepare you for any
entry level bedside nursing position (the same as an ABSN program). Discussions on this board so far suggest that "direct entry" CNLs (the type of program you describe, as opposed to experienced RNs returning to grad school) typically start out in traditional "new grad" nursing positions, anyway, and work into a CNL role as they gain more nursing experience.
Best wishes for your journey!