How do I run steam and my steam games on a school Mac?

I have an external hard drive and copied all of steam from program files to the external hard drive.

I wanted to know if I could just plug in the external hard drive into the mac and just run steam as well as my steam games onto the school computer

I tried downloading steam into the school computer directly but it needed the admin password to put it in applications

Would it work or not? Thnx in advance :)