Yes, once you have added the videos you want to transfer you can close the tab or browser and the tool will keep working until the job is done. You can always check its progress by simply open it up again.
How much does it costs?
The pricing is very straight forward. You only pay for what you use:
0.02€ per GB storage used per month (based on the average usage that month)
0.10€ per GB network traffic (only outwards traffic is counted)
8 hour stream at 6000 bitrate consumes around 2.7 GB per hour so 21.6 GB in total. 21.6 GB would then be 0.43€ in storage fees per month.
What kind of content can I backup?
You can backup any video content from Twitch
Vods (Past broadcasts, highlights and uploads)
When backing up VODs the backup will also include the stored chat on that VOD.