This is already possible through kind of a hidden feature in Photoshop minus the "server". Just wanted to share. This is how I preview most of my site designs as they end up in the browser anyways...
In Photoshop: Go to File / Save For Web...
Yes but this us live, and doesn't require any action from the user.
The newest sketch update will be getiing this feature, so if any PS users are feeling left out, here's the solution.
p.s. I haven't had a chance to try it yet.
It's a bit of a faff but this works:
Select Artboard > Click 'Export' in right sidebar and drag the preview image over to a browser address bar.