Is it possible to sync custom fonts between macOS and iOS devices? I am curious as to whether it is possible to synchronise custom/downloaded fonts from macOS High Sierra to an iPhone?

From what I understand, if both devices meet the requirements for Continuity they are capable of implementing the Handoff feature. This means a document (containing the custom font) started on the mac will show the same custom font on the iPhone, correct?
Is it possible then, to reverse the logic such that custom fonts are always synced between both devices, without employing the use of the Handoff feature - making the fonts available in other iOS applications?

The Handoff feature is just an example of what looks like font synchronisation but what I am really interested in is a way to copy/sync a font from the macOS device to the iOS device if it does not exist there (e.g. downloaded fonts). Making it available on a system-wide level (not per application) to each application capable of creating/displaying rich text.

I am interested in this from a security point of view to learn whether file types like fonts can be just as easily synced as Contacts and similar cloud-based content.
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.