Is backing a website by a SQL Server 2012 OLAP cube considered reasonable?
You could do this with an OLAP system - some of the benefits of SSAS for this type of application include:


SSAS can readily scale out - especially as this is a read-only application with no requirements for cube writeback.
Aggregations can be tuned to minimise the I/O allowing the cubes to be tuned for efficiency.
OLAP client software and third party controls (web and rich client) are readily available from a number of vendors.
SQL Server 2012 Business Intelligence edition has pretty much all of the scalability features for SSAS, so it can be used as a cost-effective platform to front cubes for a SQL Server enterprise edition (or third party) database.  Note that licensing may be an issue for this as B.I. edition is CAL-only.
SSAS has a data mining function that could be used to do a shopping basket analysis on the data and feed a 'suggested purchases' feature on the website.


On the other hand, the requirement is to show a relatively constrained data set, so the ad-hoc slice-and-dice capability of an OLAP server may be overkill, both in cost of software and cost of the hardware infrastructure to run it (SSAS is quite resource hungry).  You could probably achieve your immediate requirement with a periodically refreshed summary database, and do it with less hardware and licensing costs.

From a first glance, I would suggest OLAP is probably not necessary to fulfil your existing requirement.  However, it could certainly be done this way and you might get some mileage from the data mining features to provide a 'suggested purchases' feature.