Is an MDF "Last Modified Date" affected by transaction log backup?
My understanding is that the 'Last Modified Date' of the MDF file (in Windows) is only changed when the Database is Closed/Reopened or data is written to the MDF file causing it to grow (eg. by a Full Backup or Transaction Log Backup, assuming database recovery mode is full)


You are correct for the first part but why would full backup or log backup change "Last Modified" time of mdf file. Its actually reading from the data file its not making any changes. Normally in daily operation SQL Server reads quite often from data file but for every physical read it is not going to update the time stamp or modifiy the date that would be unnecessary.

Moreover the way SQL Server access the data and log file are not that straight it uses different mechanism so I guess its useless worrying about modified date.


  What if there was no write activity captured in the log during that hour? Would it not affect the .mdf modified date? 


NO it would not


  And if this is the case, would the modified date for readonly databases (databases that are defunct for write purposes but still used for read purposes) ever change?


Well it can change when database is taken offline and brought online and after service restart