Hi, not familiar with blocksapp, because it's only for Mac, but if it is similar to other programs like this, it should export full HTML theme.
Then you need to port HTML theme for e107. You can't upload those files directly to e107 theme manager. And for sure they will not be fully editable. So you need to take sourcess (css, js) and html markup and create custom e107 theme. For editing you need to use tools/elements in e107 (like menus, pages) or build your own stuff.
Quick Export is enough for you while developing theme,