I created a test site with the Avada theme and the Avada Toolset integration plugin and didn't experience any problems viewing either the default logo or an uploaded custom logo, whether the integration plugin was active or not.
Can you confirm which versions of the theme and plugin you are using? And your WordPress version is up-to-date at 4.5.2?
If you are experiencing the same issue with the other integration plugins I suspect another plugin is creating a conflict, otherwise there may be a server issue.
Can you please deactivate all plugins except for the integration plugin, you shouldn't need anything else active just to test the logo. Use the Avada options page to set your logo and confirm whether or not it is visible on the front end.
If so, reactivate your plugins one-by-one, testing each time, until you establish the source of the conflict.
If not, can you in your browser console inspect the logo (or broken image) to verify what the src is for each?