As of right now I can’t see a way to automatically add alt tags to images.
IMO – I don’t think you would want to “automatically” add alt tags as the alt tag for the same image could be different depending on what page / post you put it in.
Instead – I think a “bulk editor” would be the way to go.
I have emailed (about 10 minutes ago) YOAST a feature suggestion to add a media “bulk editor” that would allow us to easily change the title and alt tags on images. I have suggested that the editor could be sorted by “attached images” (those that are in posts or pages) – and “unattached images”.
If an image is “attached” – the editor could display (and allow you to change) the page title, h1, and meta description.
This would be a feature that could be included in the premium version (as I think it’s something those that are serious about SEO would pay for).
Let’s keep our fingers crossed and hope that someone at YOAST see’s my suggestion, likes it, and decides to implement it. ??