Block size depending on transaction count
Is the estimate above correct, or am I missing something?


Your estimations seem (more or less) fine.


  If it's correct, what are the impacts of switching from a 1 MiB block size to 586 MiB?


The two major ones I see are:


large blocks make full nodes more difficult/expensive to operate (i.e. requires better specs and better upload/download speeds); thus bad for decentralization as not many people will be able to run a full node
the blocks will take longer to propagate through the network, thus it increases the chances of orphan blocks and double spends.


For a more detailed list see here.

Note, that these concerns/drawbacks for an increased block size were raised for a 4, 8 or 32MBs increase... a 586MB increase would be way too excessive. And if you keep the parameters similar to bitcoin you would have the same issues in the side chain.