Listen to the Dom.....
You are exactly right. Put your app in if you're close as you never know. When they are short and get the word to hire some bodies, your CV might just arrive on that day. 20 years ago I did that exact thing, sent my app to JAL, even though they were only hiring current B-747 Captains. To my surprise, with nothing larger than an A320 under my belt, I found myself as a 34 year old kid sitting in class as a DEC on the whale . Too cool.