The short answer is yes, you can operate the machine without constratints while it is receiving sysex data.
Before I go to the long answer, I would like to get more specific about the terms used in the Octopus context.
Pages are "containers" of 160 steps each, that are played per default as 10 concurrent Tracks of 16 steps each. There are 144 pages on the Octopus, making up the Grid. The Grid is grouped in banks of 16 pages per bank (a bank corresponds to a horizontal row). At any point in time you can play only one page per bank, so you can have up to 9 pages playing concurrently. Hope this makes sense so far.
There is no notion of a song – that would be the result of your interaction with the machine over a period of time.
Now – you can upload state data to the Octopus at various levels: pages, and globals settings. Pages are play data which you would want to upload while the sequencer is playing.
When you dump out a page, it remembers the position it was at in the grid, so when it comes back via a dump-in, it will replace the content of the page at its old position as soon as the transfer has finished.
So, if you want to replace the current play data, that will work. If you want to replace data that you have played with, but that is not active (pages that are not playing) you can do that on the side, and have other pages play during the transfer. Interacting with the playing pages is always possible, the machine will not lock up during the sysex transfer.