Does OS X Yosemite support spotlight on network drives?
Indexing of an AFP-network drive isn't a problem:

To enable spotlight indexing on a network drive open Terminal.app and enter:

 mdutil /Volumes/name -i on


To disable the indexing of a connected network drive:

 mdutil /Volumes/name -i off


To check the status of indexing on a connected network drive:

 mdutil /Volumes/name -s


Source

In the comments there, a Synology NAS has been mentioned explicitly:


  MacHouis • a year ago
  Thanks a lot, it works very fine :):):). I had to mount the volume (a Synology Ethernet server) in afp to start the Spotlight Indexing... thanks thanks thanks...


This also works for older Mac OS Xs (in the example below it's Lion). Make sure that you've switched to 'Shared' in the search window: