Transaction Log Backups
would there by any TR Log Backups for that time period?


If there is no activity at all, there would be not transactions. But there is no harm in taking that backup as a part of your backup schedule (which is every 15 mins). 

It will look like - 

/*Processed 0 pages for database 'logbackup_test', file 'logbackup_test_log' on file 1.
100 percent processed.
BACKUP LOG successfully processed 0 pages in 0.072 seconds (0.000 MB/sec).
*/



  what would happen if I happen to restore those transaction log ?


You will be able to restore them in sequence or you can possibly skip it as well- if there is NO gap in the Log Sequence Numbers of the log backups..