Sadly, no. Blocks are stuck on the page you create them on.
I think the most likely iteration of a solution to this problem would be an ability to “clone” or copy a page, then you could remove the undesired set of blocks from each and end up with the contents of the original page split between two.
To be clear, the Exhibit Builder also doesn’t let you clone a page, but that feels like the most attainable solution from the perspective of the interface, as it would only “cost” us one extra button. Actual free movement of blocks between separate pages would require a much more major rethink of the way the plugin presents the blocks for editing.