Is it possible to sync custom fonts between macOS and iOS devices?
No, you're not exactly correct. 

Most app developers will make sure that both the macOS and iOS versions of their program display the custom font. This is done using either font embedding (i.e. the font is stored inside the document), or using streaming, which is a Handoff-feature that allows for the source program to transfer larger quantities of data to the destination program.

Some app developers have not invested the time necessary to do this, or are constrained in other ways. In those cases the document will show up with a wrong font on the destination device.

As such, there's no automatic, iOS/macOS handled synchronization of fonts taking place during Handoff.

In general, you can add fonts to the system font library using configuration profiles. This is intended for enterprise usage where iOS devices that are supervised or where it is otherwise accepted to install configuration profiles. This way they can have for example the company's own font installed. In the case of iOS devices managed by for example an MDM system, you could say that it is possible to "synchronise" fonts from a Mac. 

These fonts are available to use in apps that support choosing from the system library. Not all apps do this! - However apps like Pages and Numbers do support it.

To create a correct configuration profile with a font payload, you'll need a code signing certificate - otherwise the user will get a lot of warnings when installing the configuration profile. The user must install the configuration themselves by agreeing to the installation in System Preferences (you can send them there by the way of a link or similar).

For home users the easiest way to install a font is probably using a third party app such as AnyFont! or similar. 

If you're interested in specifically whether an ordinary user can select somewhere that all the fonts on their Mac must be available on their iOS device - then no, no such synchronisation method is available on standard iOS.