Hello everyone, I'm pleased to say yes, you can. I've been using iFont on the iPad.
This uses system profiles to plug the fonts in to the OS. Fonts then show up in Designer and Photo, as if you had just enabled them in FontBook. The app also has preview and organization tools.
My type library lives in iCloud, so i download to ipad and import to iFont as needed to review groups of type. My kit is mostly .otf and old .ttf and iFont works with everything i've fed it so far.
iFont is also networked with DaFont, 1001FreeFonts, Fontspace, and Google Fonts.
Edit: tagging @AppleGrove, @Dan C, @edwardsson for your interest
AppleGrove, to two of your points: this too uses profiles, and i have not seen organization/groups of fonts as viewed within the Affinity apps, but neither does my desktop do this. I rely on iFont to group / tagging and do not find loading the profile cumbersome.