Should I send private email to department's dean after sending faculty job application? There is one exciting job opportunity that I am willing to apply.
The dean, I think, may know me because I have met him in a couple of conferences and I have been on a discussion panel once (as a Ph.D. student) in a conference which his department organized. 

But he is a big shot, and he may know a thousand young aspirants like me. Will it be wise to send him an email or will it give a bad impression that I am trying to cajole him?
If you really know him and have corresponded otherwise, then it would be fine. Otherwise I wonder, as would everyone else, what you are trying to accomplish. 

But you haven't said that you have actually applied. The title is a bit inconsistent with the first paragraph. 

However, if you get an email, after applying, thanking you for the application, you could reply to that, reminding him of your earlier connection. But it would probably be improper of him to take any action other than what he would do for any candidate. Likewise, if you get an interview, you could go visit him. 

But probably not a cold email. Especially since you raise it as a potential issue.