Working on TestComplete while TestExecute running

If you have TestComplete on one and TestExecute on another and are executing your test on the test execute machine... Yes, you CAN work on editing it while it's running.  However, you might run into some problems saving some changes because there are some files that are marked read-only during a test run or that are updated dynamically during a test run that, while you are working on it, you will either be unable to save or you will over-write something the test execution is using.

Best practice is what someone has already suggested.  If you want to have your project stored on a shared drive for TestExecute to run against, that's fine.  But for your editing purposes, you should check out a copy of your project to your local hard drive and go through standard check-in/check-out source control procedures to put your code into the main project.

The way I like to think of it (since what you are essentially doing is writing script code) is that you would not edit script code on your production website while it was running. You'd make your changes to your script code in a development environment and then, once it's completed, integrate it into your production environment.