Ciao Dodo87, have you already synced your watch with the strava app? As far as I understand from your question you shouldn't experience any issue. 

So the answer is yes you can

Hi ​@Dodo87  - sorry we don't speak French here (well, not most of us ) so just to double check, from Google translate it seems that you actually want to export a route GPX from Strava to your AW, right?

I’m afraid that is not possible, but there's a feature request open for voting: 

As an alternative, some athletes are using e.g. the WorkOutDoors app, and then sync their activity to Strava from Apple Health (instead of recording it directly with Strava). 

hello ​@Dodo87 - did any of the comments above help? if so, let us know! :)