The invite link will NOT be the same for a customer when using each of these tools. The Bulk Invite tool and the Link Generator tools are not intended to be used simultaneously, however they can be used sequentially.
For example, you could use the Bulk Invite first to send out invites to your customers. Then, a week later, you might want to generate links for your customers and send out invites through your own email platform. This would work fine, however there is one caveat: the reason they can’t be used simultaneously is that when you generate the links for the second batch with the link generator tool, the activation links from the first email batch become invalid, as Shopify will generate NEW links for those customers when you use our link generator tool. So any customer that clicks the link on your first bulk invite will get an error message, so make sure you wait a sufficient amount of time between sending out batches of activation emails if you decide to start with our bulk invite tool and move to generating links for your own email platform.