No, it detects the screenshots as you take them. (I helped build the app)

So every screenshot I take on my iPhone is automatically imported into SnapUp / sent to your server?

No, we do some client-side prefiltering to ignore non-products, and we also do some more extensive server-side filtering. We also allow you to cancel snap processing, as well as go into an "Ignore new snaps" mode via the settings in the app. Also, the upload only happens when the app is foregrounded, giving you further control.