Etiquette - APS jobs high above level

An EL1 job is open that I'm on paper qualified for, but I'm currently only an APS 5. I don't think for one moment I'd get it if I applied but is an application going to be looked on unfavorably? The job doesn't require supervisory experience, and I have all the other qualifications, but it would be a promotion two levels and I know that never happens. I am thinking of putting in for it even knowing I won't get it to get my name in the mix but I'm worried it will look like I'm not serious and that I'm getting lofty ideas. Is it worth it anyway or will it just waste my time, their time, and make me look arrogant and jumped-up?

(Not in CBR any more but I know this community will know more about it than anyone else.)