There is a “premium desktop” app that is not made available as part of the trial period (as far as I could see), so I can’t comment on the file size or connectivity requirements. But it seems reasonable to assume that yes, you have to be online. I also have a limited amount of faith in the StackSocial offerings, nor is there any sort of an easy way to figure out what “$99 lifetime subscription” translates to in monthly costs.
The WS site offers the online-only solution for $9.95/mo or $6.66/mo if you prepay for a year (and $4.44/mo if you prepay for three years), and the premium desktop version for Windows and Mac for $14.95/$9.99/$8.33, respectively. The mobile app is an add-on for $2.50/mo, $9.95/yr or $30/3 yrs. Which seems kind of strange, given that you’re paying more for three years at once than you would for three consecutive one-year subscriptions. Not like the company is allergic to non-whole dollar amounts…