Does Exchange support disposable e-mail addresses?

Solution 1:

Out of the box no.

You could develop an event sink that does the routing for you... This might get you started.

Solution 2:

This feature is now available on Office 365 Exchange!

Exchange admins will have to enable this manually on their server. This can be done through Powershell using the following command:

Set-OrganizationConfig -AllowPlusAddressInRecipients $true

For instructions on how to use Powershell, you can find out more here: https://docs.microsoft.com/en-us/powershell/exchange/exchange-online-powershell-v2?view=exchange-ps

The setting may not instantly take effect so please expect a delay before you can start using plus addresses.

We're still waiting documentation on this feature and from feedback I've seen, it doesn't work for everyone currently.