Would police be able to recover these emails?

Your Outlook files are kept on Microsoft's servers. They tell you they are deleted but it can still take a few days for them to get around to deleting them. This for people who change their minds. But even after this date they will publicise that they are deleted just to stop people pestering the help lines all the time.
Don't forget that the NSA keeps copies of all emails. The police generally don't have access to these because it is too much bother for a trivial crime. But if you are involved in something more serious the NSA will pass the information to the police.
When deleting files that moves them to the trash. You also need to empty the trash.
There could still be remnants of the files on the computer's hard disk. Deleting a file doesn't actually clean it from the disk. The space is just marked as available for overwriting by something else. Until it is overwritten the information can be recovered. Even if parts of the file are overwritten some scraps may be recoverable and these scraps could contain important information.
That's why (at least on a Mac) there are two options for emptying the trash. "Empty trash" and "Secure empty trash", the second option takes much longer because the disk needs to be overwritten a lot more.
Also this does not erase information in temporary files that are created to save memory, it often does this when you have several apps open.
So if you have viewed something that would be of interest to the police you should then always remove the hard disk before allowing anyone else access to the computer, especially if you need to take it for repair. The repair shops have a legal requirement to search your disk and pass any information they find on to the police. The best thing to do here is keep a second emergency disk that you can switch in for these sorts of situations.

If you used a mail program like Outlook Express or Thunderbird then your emails are stored on your computer and you do not need the police to recover them. If you were accessing the emails through the web interface then the emails are stored on the Outlook servers. If the police were to suspect you of a crime and thought your email account contained evidence of the crime they could contact Outlook and request access to your account.