Installing Hybrid Exchange Retrospectively?

Well it's  hard to guess as I have no idea how your AD looks like, but in general, it's doable and shouldn't break things. The first thing you need to do is extend AD with the Exchange schema attributes and refresh the AAD Connect schema. This will allow you to edit all the Exchange related attributes from on-premises. You can "match" the already existing users and have everything managed centrally from AD.

From there, you can decide which route to take in terms of actual management. Hybrid is not a requirement for that. Technically, you can manage everything just fine once the schema is extended, as long as you feel comfortable using ADUC or PowerShell to do so. You don't even need to have an Exchange server installed, just the schema. The problem with this approach is that is not supported by Microsoft, meaning if you run into some issue, they might deny you support. If you want to be in supported configuration, you need to have at least one Exchange server for management purposes. But that adds some overhead, and some organizations prefer to simply use the AD tools instead.