No conflicts would arise with your CRM application if you migrate to Office 365
This resource would help you to migrate from Exchange to Office 365.
Setting up an email cutover migration to Office 365 requires careful planning. Before you begin, here are a few things to consider:
1. You can move your entire email organization to Office 365 over a few days and manage user accounts in Office 365.
2. A maximum of 2,000 mailboxes can be migrated to Office 365 by using a cutover Exchange migration. However, it is recommended that you only migrate 150 mailboxes.
3. The primary domain name used for your on-premises Exchange organization must be an accepted as a domain owned by you in your Microsoft 365 or Office 365 organization.
4. After the Office 365 migration is complete, each user who has an on-premises Exchange mailbox also will be a new user in Office 365. But you’ll still have to assign licenses to users whose mailboxes are migrated.
You will find rest of the details over here.
I hope this helps!