Does a database update force index rebuild regardless of updated field?
First, have a look at the InnoDB Architecture (From Percona's CTO Vadim Tkachenko)



When you update an indexed column, changes must migrate through this architecture as follows:


From Insert Buffer section of the Buffer Pool to the Insert Buffer inside ibdata1
From Dirty Pages of the Buffer Pool to the Tables Physical File (.ibd file)


If you are updating a non-indexed column, the only bottleneck would just be the flushing changes in dirty page over to the .ibd file over the Write I/O threads. Index change buffering would not be involved for non-indexed columns.

If you have MySQL 5.5/5.6, you may want to increase innodb_write_io_threads and innodb_log_buffer_size for increased write performance.