In all organizations where IT is not the core business, IT has a support role. It merely supports the business in doing what results in company profit. The quality of this support will therefore depend on the way IT manages in understanding the operations of the business. From this point of view, it is very hard for IT to impose an IT language (such as UML, Use Cases, etc) to the business as the language to use towards IT.
However, introducing business processes in an IT department as a valuable asset they can work with, is not as hard as you may think. Most IT departments do model the behaviour aspect, the information aspect, and the business rules, when it comes to modelling business requirements for automation projects. Providing them with well modelled business processes, will majorly facilitate and speed up the analysis work they have to do anyway.
When a business process model is used as reference base, imho, the importance of the implementation methodology also diminishes. Evangelists often promote certain methodologies such as agile to be the way IT can prove business value. However, with a proper process model, the business has a clear overall view on what they want to realize and where the important points are. Whether a waterfall, iterative or agile methodology is used to make this happen, it is just a matter of delivering what is defined before, in a timeframe acceptable for the (business) customer.