Does `Enable Messages in iCloud` sync historical messages from computer to phone?

My phone was sadly stolen recently. I bought a new iPhone and much to my chagrin, had not yet setup iPhone Backup, so I'm starting from basically scratch.

My photos synced across, but the only thing that didn't is my iMessages. I have them all on my laptop, but they are not populating on my phone. I have followed the instructions here: How to transfer iMessages from Mac to iPh… - Apple Community to ensure that both my Mac and my Phone have `Enable Messages in iCloud`.

I'm curious if it will only download new messages and share them across (which was working already), or if historical messages will also sync across. I see the `Downloading Messages from iCloud` in my Messages, but that doesn't indicate a two-way sync.