SQL Server - Migrating a SSAS-less Data Warehouse to SSAS

I was tasked with creating a reporting tool for a company which crossed multiple business units, applications and databases.  The client had SQL Server 2012 Standard so educated myself on the MS Business Intelligence tools.  In the end I used SSIS to bring the data into a single database, SSRS to report off these tables and a web front end for users to select reports and provide parameters.

While I wanted to use SSAS, time constraints and my current skill set required that I get something up and running.  I delivered and though some of the larger reports have performance issues it was a successful project.  

So currently I have a SQL Server BI Solution which does not leverage SSAS.  My question is, once I come up to speed with SSAS does it make sense to use the non-normalised tables I have created for direct reporting as staging tables for SSAS?  My reasoning is this would let me move to SSAS in stages.  I wanted to take advantage of the benefits of SSAS performance and functionality but am keen to leverage the work invested to-date.

Sort of an aside question; how insane is it to be in this situation?  I'm curious if this is a normal progression to SSAS or if I would be institutionalised if I mentioned this at a conference.