It defaults to C:\EEK. I don't know if that's changeable at installation. I didn't try that.
There appears to be that option, see the attached image in my Reply #3.
In that case, there isn't any reason why you couldn't place EEK on your USB.
Well it would appear there is a very good reason not.
I created an EEK folder on my 8GB USB stick and ran the installation file and pointed it at the USB EEK folder. It took a very long time to extract and copy files to that folder.
Next running the 64bit executable to start, that too took some time and then suggested checking for updates, which I did and that took even longer, checking for updates and latest definitions, etc. etc. When the scan started (I had elected not to scan for PUPs and the shortest scan) it took quite some time calculating what would be scanned.
I went off and left it to run, despite having not to scan for pups, it reported what it considered a PUP entry in the registry (from the information shown, there really wasn't any way to determine that) and I unchecked that. I got a few messages 'had my AV let me down' etc. etc. (which I closed).
All in all this isn't an experience I would be prepared to do every time, too much hassle. For me it is dead in the water, certainly for a USB installation, I'm not even sure I would like to install it on a hard drive (certainly not on my primary SSD drive).