Can the LOG file fill up from index rebuilds where the indexes are not fragmented?
My question is this, can automated index rebuild jobs that run hourly fill up the log file?


Yes. An index rebuild typically rewrites all of the data contained in the index. I don't know of any exceptions, but there might be some. From the documentation:


  Rebuilding an index drops and re-creates the index. This removes
  fragmentation, reclaims disk space by compacting the pages based on
  the specified or existing fill factor setting, and reorders the index
  rows in contiguous pages.


You also asked:


  My assumption here is that the index would not be fragmented and so there would not be any work to rebuild the index. Therefor, the log file should not fill up. Is this assumption false?


Fragmentation does not matter because a new copy of the data is created. You may be thinking of the REORGANIZE command. The amount of work performed by that command depends on fragmentation of the data, but it's done in small transactions.