Yes and no. The Tablo application… no… there is limited access to file/media data via url though.
For example if you know the Tablo rec_id number for the program you can access the m3u8 playlist like so:
http://<your-tablo-ip>:18080/pvr/<rec_id>/pl/playlist.m3u8
You can use a program like SurLaTablo to easily search the media on your Tablo and get the rec_id.
surlatablo.py -q 'The Flash' -Q '${rec_id} ${friendly_title}'
640819 The Flash - s02e16 - Trajectory
585734 The Flash - s02e13 - Welcome to Earth-2
578003 The Flash - s02e12 - Fast Lane
570517 The Flash - s02e11 - The Reverse-Flash Returns
563160 The Flash - s02e10 - Potential Energy
518477 The Flash - s02e09 - Running to Stand Still
518476 The Flash - s02e08 - Legends of Today
497168 The Flash - s02e07 - Gorilla Warfare
So… some limited access is available.
Of course, this is SurLaTablo, so maybe this output is more convenient:
surlatablo.py -q 'The Flash' -Q 'http://<your-tablo-ip>:18080:/pvr/${rec_id}/pl/playlist.m3u8?title="${friendly_title}"'