If we’re only looking at the Japanese side, there are indeed a couple cards exclusive to the theme decks. Probably about halve the cards were exclusive to one of the decks, and the other halve were also available in the sets.
To give an example: Brock’s Zubat was only available in the Nivi City Gym theme deck, and not in either of the two Gym sets (Leaders’ Stadium and Challenge from the Darkness).
You could open the individual links on Bulbapedia on each of the deck pages and see which Japanese sets/deck the card has been released in. The six decks pages are: Nivi City Gym (Brock); Hanada City Gym (Misty); Kuchiba City Gym (Lt. Surge); Tamamushi City Gym (Erika); Yamabuki City Gym (Sabrina); and Guren Town Gym (Blaine).
To use the same example again, Brock’s Zubat was only available in the Nivi City Gym theme deck, and Brock’s Vulpix was available in both the Leaders’ Stadium set and Nivi City Gym deck:
What you should and shouldn’t count for your own collection goals is completely up to you. 
I personally do count the no rarity versions of the theme decks as different versions, just like I’d do with the Japanese no rarity Base Set cards. It’s fairly similar to collecting both a 1st edition and unlimited edition version for the English sets imo.
Here are the Pikachu (two from the Lt. Surge’s theme deck and one from the Leaders’ Stadium set) from my own Pikachu collection:
But it’s your collection, so collect however and whatever you want. 
Small correction, only the first two theme decks (Brock’s and Misty’s) were released on that date. The Lt. Surge’s and Erika’s theme decks were released on July 25th, 1998 and the Sabrina’s and Blaine’s theme decks on February 26th, 1999.
Greetz,
Quuador