No.
You can’t be reasonably sure your outgoing email will be delivered, as many destinations simply blacklist, firewall, or even null route all major cloud providers’ IP blocks due to the heavy abuse seen from those ranges – not just from email but via other services as well.
And even if your mail is delivered today, that’s no guarantee it will continue to be delivered in future.
You really do need a mail server outside of Azure (or EC2 or whatever) to process your outgoing mail, though it does not necessarily need to be a third party mail server. If you have the expertise, you could do it yourself.
When I put a service on EC2 which had to deliver to a mailing list, I found from testing that almost 3/4 of the list addresses would not accept mail from there. I ended up sending everything to a smarthost located outside EC2. Interestingly, this also improved performance…
Having incoming mail on Azure would be no problem, as the above issues don’t apply.