We are migrating from Sitecore v7.2 to v9.1. We would like to migrate customer xDB data on Azure. Can we automate using xDB Data Migration Tool?
In short, No.
In Sitecore v7.2, Digital Marketing Suite introduced a lot of concepts around personalization and rules-based marketing. Additionally, early versions of the Email Campaign Manager (now called Email Experience Manager) provided an early concept of contacts but was never formalized as a central repository of marketing data.
Sitecore 8.0 introduced the Sitecore Experience Database, or xDB, and overall new integrated marketing platform, including List Manager and the idea of Contacts being kept in xDB. Email Experience Manager, which was rebranded and redeveloped as a separate module, had a tight integration layer with the overall Marketing Operations Center of Sitecore 8.0. The biggest challenge in Sitecore 8.0 was that access to xDB data was only through specific Sitecore API's and customizations of external interactions were extremely difficult to near impossible.
Sitecore 9.0 introduced the concept of xConnect, which was a much-needed service layer separating Sitecore and xDB so that external interactions and access to contact data could happen. Additionally, Email Experience Manager was brought native into the product line as well (as of 9.0.1)
xDB Migration Tool
The xDB Migration Tool was introduced as a module addon to the Data Exchange Framework that allowed modeling of contact and interaction data from Sitecore 8.X xDB (which was kept in Mongo) to Sitecore's 9.X xConnect service endpoints (which can be SQL or Mongo). This module has a few different versions based on the Target version of Sitecore, however can migration xDB data from Version 8.0 and higher.
So where do you go with Sitecore 7?
The real answer is that you are abandoning the Sitecore 7 analytic data and starting over in Sitecore 9. The time, cost, and effort involved in trying to upgrade Sitecore 7 to the latest version of Sitecore is not worth the data (and in some cases the lack thereof) that you could possibly get out of Sitecore xDB in Sitecore 9.
But it's possible right?
Technically, anything is possible. Following the entire upgrade path from Sitecore 7.2, which requires you to traverse a large portion of many installs of Sitecore 8.X, and a light touch analytic migration from 7.2, will allow you to get some data from Sitecore 7.2, but this would likely be a 1-year project for little effect. If there's Email Campaign Manager in play that is intended to save, along the upgrade path in Sitecore 8.1 - Update 1 and 8.1 Update 2, you lose analytic data anyways as part of the upgrade process.