Please note that this article is applied for the case you converted the quote to a draft order.
Next time, if you edit the quote and send an email to customer, you do not need to go to Shopify Draft orders and review the draft order.
All the changes you save after editing quote will be automatically updated in the Shopify Draft orders.
For more information:
If you made any changes to the draft order, then by default a notification is sent automatically to your customer. You can disable this notification from the Notifications page in the wholesale channel. You can also contact your customer directly to make sure that your customer approves of the changes before you send an invoice and start the payment process.