Karan Bhatt, thank you for posting this question on Microsoft Q&A.
Based on your question, I see there are 2 parts to it and the corresponding responses are below:
- Throttling issues in Email - This is more of an Exchange specific troubleshooting scenario and troubleshooting from Exchange side can help you in this regard. Azure-Arc has nothing to do with this case. Azure Arc helps you connect your on-premises machine to Azure platform, so that you can manage/monitor them similar to Azure VMs (within supported scenario).
- Update issue of the Exchange 2013 - In case you are looking for updating the on-prem Exchange 2013 servers itself (including the Windows OS and other Microsoft Softwares like Exchange etc.), you may use Azure-Arc to onboard this machine to Azure and then use "Azure Update Manager" to patch these servers.
Hope this helps.
If the answer did not help, please add more context/follow-up question for it. Else, if the answer helped, please click Accept answer so that it can help others in the community looking for help on similar topics.