Yes, OMGF Pro is compatible with Avada. The free version of OMGF isn't, due to the way Avada includes Google Fonts into the theme.
First off, you need to make sure that Avada doesn't use its own local storage method (it's kind of faulty and doesn't load all fonts locally):
Go to Theme (Avada) > Performance > (4) Fonts and set Google & Font Awesome Fonts Mode to CDN. Make sure you click Save Changes. Clicking Next Step won't save the changes.
Second, which settings you have to enable in OMGF Pro to make sure Avada's Google Fonts will be properly detected depends on your CSS Compiling Method setting, which can be found under Theme > Options > Performance or, Avada > Performance > (6) Optimization in recent versions.
The CSS Compiling Method setting has 3 different options. Database won't work, because OMGF Pro doesn't scan the database for Google Fonts (mainly because, who saves CSS in the database!?)
When File is enabled, make sure that OMGF Pro Advanced Processing (Pro) (located under the Detection Settings tab) option is set to Process Local Stylesheets.
If CSS Compiling Method setting is Disabled, Avada will insert all the compiled CSS inline, so make sure Advanced Processing (Pro) is set to Process Inline Styles.
If you already ran OMGF Pro's Save & Optimize routine, make sure you empty its cache directory and run it again to make sure OMGF Pro the changes in Avada's configuration are processed in OMGF Pro as well.
That should do it!