No. But you can add a logger plugin.
Emails send when the order status is changed to ‘processing’, ‘on-hold’ or ‘completed’. Check your orders have this status.
You can see if emails are ‘sending’ but you’re just not receiving them with https://wordpress.org/plugins/wp-mail-logging/ Don’t forget to check your spam box.
If not spammed, but logged as sending, it may be a server issue. Try using a different method of email sending with https://wordpress.org/plugins/wp-smtp/
You can also combine https://wordpress.org/plugins/wp-smtp/ with https://www.mandrill.com/ or https://www.mailgun.com/ for improved deliverability and logging. I recommend this anyway.