Yes, it very well may be checked on a database. Additionally, if this isn't the first assignment you've turned in, you're taking a risk that the instructor will notice that the plagiarized essay isn't in your writing style. Whenever you use an essay lifted off of the internet, there's a chance that previous, or even current students have turned the same essay into the same professor.
I completely understand how busy and overwhelming graduate school gets and I'm not trying to sound like a goody two-shoes when I tell you that plagiarism is a huge offense. As a former college instructor, I've failed students for plagiarizing and as a graduate student, I've seen other candidates fail classes and even get kicked out of programs for attempting to plagiarize.
Beyond the moral/ethical issues of taking other people's work, it's simply not worth the risk. Even if you're on an impossible time crunch, it's better to contact your professor and ask for an extension, or even to write a subpar essay. A hastily-written essay will still get you some credit, whereas a plagiarized essay has the potential to not only earn you a zero, but potentially get you booted from the class altogether.