It looks like if we add:

remove_action( 'edd_customer_post_attach_payment', 'edd_connect_guest_customer_to_existing_user', 10, 4 );

to the batch payments import init function, it will prevent the emails from being sent.

Noting also that I'm getting quite a few PHP errors when some payments are imported, starting with:

PHP Notice:  Undefined variable: customer in \plugins\easy-digital-downloads\includes\admin\import\class-batch-import-payments.php on line 455

Note: we need to also make sure that the users are not marked as pending (needing verification) during the import process. I think they won't be, as that happens within the edd_connect_guest_customer_to_existing_user function, but noting to make sure we confirm.