Hello Solid!
Yes. You can export your past broadcasts and or highlights with a smart phone and possibly a tablet. Just as long as you have a browser to go on Twitch’s website so you can go through the necessary steps to export your video. In addition, you can even go to your local library, where they have desktop computers and do it from there. Nothing will be needed save on that computer or device because your video will just export straight to YouTube.
Sadly, Xbox One does not have this feature…but it would be awesome to have!
If you have any questions on how to export or anything else, do not hesitate to reply. 
Have a great day!
- Walter