Yes; JR-West Kansai-Hiroshima Area Pass, unless you have a ride on the Ordinary Class reserved-seat part or you get into a Green Car, allows you to take Shinkansen and other Limited Express trains inside the usage area.
There is no JR fee which is to be called as seat fee.
(HyperDia shows this misleading term "Seat Fee" in search results.)
You pay a surcharge for a JR Shinkansen or Limited Express service,
and its price differs by whether your seat is reserved or not;
JR companies do not call this difference as a fee.
When your seat is reserved on a Shinkansen or Limited Express train,
JR-West Kansai-Hiroshima Area Pass covers the basic fare only;
you should pay the full amount of the surcharge,
not the gap compared to when your seat is not reserved.
- JR-West: Kansai-Hiroshima Area Pass
http://www.westjr.co.jp/global/en/ticket/pass/kansai_hiroshima/Please note that a JR-West rail pass is not valid for a Shinkansen section (such as Shin-Osaka -- Kyoto -- Maibara) on the Tokaido Shinkansen, which is operated not by JR-West but by JR-Central.
The Shinkansen zones of Shin-Osaka, Kyoto and Maibara Stations are managed by JR-Central;
at Shinkansen gates other than Shinkansen transfer gates in these stations,
a gate machine may reject a JR-West rail pass.
this means you can travel travel in the unreserved seat part of the train without any additional fees. Here this (= the pass does not include seat reservations) does not mean so.
Some JR passes do not allow you to use Shinkansen or Limited Express train services
regardless of whether a seat reservation is made or not.
Enjoy your trips!