Syncthing doesn't do smart sync. The library of stuff I want available is larger than can fit on my phone.
Maybe it's possible to implement that as an extra app though, without even touching Syncthing. Android seems to have some concept of virtual file systems provided by apps so perhaps one could on-demand un-ignore files then block until they're available. (But yeah, that's definitely more than a quick hack.)
In Dropbox, if I want a file I haven't synced yet, I just browse to it and open it. I can also mark folders as available offline.
I'm using Seafile for that now, but I don't like that it needs hosting and I'd love to switch to something P2P and get rid of the server.