The question you ask is rather subjective to the needs of the organization and how the Enterprise, Design team, Engineering team and the actual users feel about the change.
I would highly recommend you to speak to the actual users of the application first and observe how they use the app you are about to redesign, see breakpoints and frustration, ask them about what do they think is most annoying, what's perfect, etc.
After this, draw a few mockups of how your redesign would look in MD and speak to the users. Make a small prototype using Pixate if necessary and show it to the users, creative team/ UI-UX/ Engineering. Get their thoughts on it.
I have done this for one client and I can tell you that while it was very well appreciated by the Creative & Engineering team, the Top Management had different views. This was for a Tablet application for an Insurance company which was used by the company's agents.
Enterprises generally do not like animations or complex elements from Material Design guidelines, especially the Executives who prefer to have a more professional look. You need to decide accordingly to which rules you might have to bend in order to fulfill the needs of the Enterprise. Generally, executives only have pet peeves regarding few elements or the MD principles in general, and they aren't always listening to the actual users of the application who work on it for most of the time.
In my case, the Engineering team warned me against using Radio Buttons because the Executive found it to be confusing, apparently. So, I went ahead with Toggles for Gender-specific information with two options and Sliders for multiple options. Apart from that, other elements needed a color tweak for better visibility to the background white. Instead of using the Traditional date widget in MD, they needed a Calender view when the date's fields were clicked. Also had to make sure the error warning is seen immediately by the Agent so that he need not edit things after reaching the end of the form and can do it in the flow itself.
In my case, they went ahead to implement it but I don't think so it made it ahead of the Executive's decision. I would not change a thing in my mockups, but I believe it was the colors and the amount of time and learning that made them skip the design.
I believe an Enterprise application which employees use daily needs to have a little color so that one could improvise the experience and thought patterns of the user psychologically, especially for Call centers. I also think you should implement a Night Mode/ Dark mode for Call center employees who work night shifts. I would recommend checking the Material Colors Doc and choosing colors appropriately.
Also, since you are designing it for the Web, I highly recommend using Polymer which has Material elements built in.
You should definitely refer this post by Kyle Ledbetter since it goes in detail on using Material Design in Enterprise Applications.