Can a running ERP system be coupled with BI capabilities?

Yes you can, but it is really a big challenge. Integrating BI (business intelligence) capabilities with ERP (enterprise resource planning) systems need a lot of planning. To succeed in the integration you should have an efficient and single ERP system working across your organization. The integration process can be even easier if the utilization of a single BI system within the organization.

As it is a common knowledge that when you have fewer disparate systems to tie together, the easier the integration. Additionally, it helps to ensure that your master data and metadata definitions are homogeneous throughout the organization. It is also important to recognize that, while ERP systems provide a wealth of operational data, they do not paint a complete picture of your business. For this reason it's important to ensure that the BI tools you choose can be readily integrated with your mission-critical systems

Yes it is now common for any of the ERP system having built in with standard BI capabilities. The growing need of Business Intelligence and Analytics will continue to force this requirement to be provided with the ERP systems. 

Yesr, some ERPs provide this capability.