Can I fresh install a Beta version of macOS?
There's some misconceptions here.  Let's clear them up....


  Current Beta access program enables one to upgrade to macOS Mojave
  from a stable release,


No, it gives you access to prerelease software that you can install on your device.  They make no mention "enablement of upgrade."  Granted, since Mojave hasn't been released, it will be a de facto "upgrade"


  Would creating a bootable installer and booting from it be a good
  idea, when I'm working with a Beta version?


A better question would be, "Why wouldn't it be a good idea?"

A beta is, again, prerelease software and it will have bugs.  


  Please note that since the public beta software has not yet been
  commercially released by Apple, it may contain errors or inaccuracies
  and may not function as well as commercially released software.


When you download the software, you are presumed to have read and be aware of this.  There's nothing precluding you from attempting to install it via USB and it's encouraged.  Should you find an issue, report it to Apple.

And....

It's important to note that Mojave and all beta software in general is being made publicly with the expectation that you leave feedback about issues/problems/bugs that you discover.  Expecting the software to function without issue or as a fix for what plagues released software is an unrealistic expectation. 

In other words, don't run this on a "production" machine and make lots of backups of your data.