Yep. This is right in my line of business. I have a standard speech that I give to people which I'll shorten here:
"Your employer's computer system belongs to your employer. Everything you do on that computer belongs to the employer. Even if they're not actively watching you, they probably keep server logs and backup files of email which can be reviewed if they want to. Don't do anything on your work computer that you wouldn't be able to explain to your mother, your spouse, your boss, or the news media."
If an employer takes a dislike to an employee, they do two things first. They pull out the resume/job application and see if they can find any false information there. Then they look through the employee's internet activity to find anything incriminating.