Applying For Jobs Past Their Application Date

Hi all,

I recently saw a job posting I wanted to apply for but it was past the application date. I decided to send an email to the hiring manager just asking if the position was still available. I've done this before a few times and usually get an email back saying yes/no etc.

However, this time I was sent an automated generic email thanking me for my application and saying due to the large volume of applicants they can't get back to everyone etc.

Should I just send a CV in anyway? The posting is past so I'm thinking that they just haven't turned off the automated email yet but I don't think I'll get an answer regarding if it's open so maybe I should just send one in anyway?

Just wondering what other peoples opinions are on this. Like, would it be weird if they DID look at the emails and saw one from me asking if it was open and then saw another from me with a CV?

Thanks!