SfB Auto Attendant - straight to voicemail?

Agree with above. That is how we accomplish this with another onpremise pbx routing through a mediant gateway to Exchange UM in the cloud. We have 2 E3 users created in AD, in our hybrid environment. Then assign a Full E3 license and have a mailbox with UM/Voicemail setup for them. Route the call to the coverage path for voicemail for the user after the greeting off hours. Then delegate access to another user to view that account in Outlook/OWA to route/listen and deal with the voicemail that might have been left over night.

I know other cloud providers have AA with voicemail attached different that cost nothing. But for now, missing feature and only work around to accomplish what you want. So, that means $240/yr to have a user/mailbox setup with UM to get this done.

EIDT: wanted to add and clarify, our auto attendant is currently built into our Avaya S8300/G450 PBX.  But after the night AA, it just routes to the Extension for the Echange account with voicemail enabled.

I did some testing with the AA preview for the cloud, as you likely know, maybe you are in premise though, that there are several options on what the AA can do after the AA greeting. One of those options is to route to a person, which is the general/night voicemail user we have setup.  And they can leave a message.  It works with the Cloud PBX as well.  But you still need a full E3 user in O365 with voicemail enabled.  Then we delegate users to see that account in Outlook to review those voicemails left the previous night/weekend etc.  No other way this can work with MS Skype PBX except with a 3rd party hosted provider.

We are looking to move to a hosted 3rd party Skype vendor,  they state they use Exchange AA for this functionality, but it can work the same way as well.  Not sure, never used Exchange AA.  But I have looked at the options/features it uses under the UM dialplan.  It has multiple features/options on how it can route to a person, voicemail etc.  Just Exchange UM/Voicemail feature, not the AA feature, but my vendor tells me is can handle and do this as well no problems.