Nowadays it is possible to use Visual Studio Team Services from Microsoft Azure with Organization account, without having to have Microsoft Account. This is nice feature and we use it in our organization. However it seems that we are not able to activate / use Sign in to visual studio button and login with Organization account, because only Microsoft account prompt is shown.
Is it possible, and if so, how to login/sign-in/activate Visual Studio 2013 desktop program with Azure Organization Account instead Microsoft Account ?
You can now sign in to the Visual Studio client/IDE with Microsoft accounts or work/school accounts (formerly organizational accounts). Previously, you could only sign in to the Visual Studio client with a Microsoft account.
Set up Visual Studio with Team Services
Visual Studio Team Services is different service from VIsual Studio Desktop.
As of Today I am not aware of the possibility to sign-in to Visual Studio Desktop with OrgID. However, you absolutely will have no problems signing in to your Team Services using OrgID and use the Team Services from within the Visual Studio Desktop IDE.
Last but not least, Sign-in to Visual Studio IDE provide service that is absolutely different and has nothing to do with the Team Services.
Just one of all the features the "Visual Studio Sign-in" provides, is to automatically sign you in to your Team Services account. But if your Team Services account is an OrgId, then you will have to use the OrgId when accessing the Team Projects. That's it. There is no restriction on accessing the team projects.
UPDATE
Almost two years after the original answer, it is now possible to login to Visual Studio Team Services using Organisational Accounts. Check more here.
I haven't tested it myself, but you should be able to do this. You just need to jump through a few hoops to do it.
Here is an excerpt from the MSDN FAQ:
Q. Can I use an Organizational account with my MSDN subscription?
You must use a Microsoft account to activate your MSDN subscription, but you can then link your benefits to your Organizational account through the My Account portal. This way, you can use your benefits with Visual Studio Team Services accounts that were either created or set up with Azure Active Directory to support Organizational accounts. You get the same level of benefits whether you use an Organizational account or a Microsoft account.
The FAQ also explains that there is actually a benefit to doing this, as it reduces risk for the business. The reason is that the business have control over the assets created by the organizational account, and as I understand it, it's easier for the business to transfer the MSDN benefit to another account when using organizational accounts.