Yes, the integration with Gmail and the other apps is in fact very deep, and that's why we typically do not recommend hosting email externally. But it can be done. It will just be cumbersome for your users, because they have to switch back and forth between two entirely different "ecosystems".
If you host your emails in a different environment, everything inside Google Workspace that is creating Email notifications etc. will have to be routed to the external email addresses. You can find out more about the different options here:
https://support.google.com/a/answer/2685650
You probably want to take a closer look at the first delivery options, which is called "Split Delivery".
All that being said, I would encourage you to make a clean cut and put your phase 2 into your phase 1, e. g. migrate email from the get go. While Google's own email migration options are very rudimentary, there are options available from third-parties that really make this very easy. A tool like CloudM for example can migrate all your data and emails and automatically create the corresponding users for you in Google Workspace all in one go. Take a closer look at the CloudM Migrate product.
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