Most of the CatTools activities run at the device CLI (Command Line Interface) the same as if you were to manually run them (using a Telnet/SSH client).
If your CatOS devices have issues when you manually connect to them and run the 'Show Tech' command, then CatTools will more than likely have those very same issues.
How can I run the show tech-support command via cattools and have the file stored on the cattools server? as with all the other scripts?
By using the Device.CLI.Send Commands activity: http://www.kiwisyslog.com/help/cattools/act_devclisendcmd.htm you can send commands to the CatOS device and capture the output to file (which you can save on the CatTools server).
Enter the show tech-support command in the 'List of commands to be entered on the device' field.
You can probably leave all the other options in their defaulted state (unless you don't want to receive emails).
The 'Save device output to file' field allows you to change the filename/path of the captured data file (i.e. the output of the show tech-support command).
Hope this helps,