Sort of....
When you add a kata to a MA style, you are adding a specific weapon kata. The character will automatically know that specific kata when the style is acquired, even if he doesn't yet meet the rank requirements (he won't be able to use the kata until he reaches the rank requirements though).
So the style you detailed above would be
Ejvyn's Style - Tier IV Martial Arts Strikes, Adrenal Defense, Club Weapon Kata, Paired Club Weapon Kata.
And when the character learns the style, as soon as he has 1 rank, he can use the Club Kata (and he knows the Paired Club Kata automatically).
The Katas that are part of the style are learned automatically, for free. To learn any additional Katas, the character will have to pay DPs and have the minimum number of required ranks in the style.
So, to learn, the Dagger Kata for his style, Ejvyn will need 5 ranks in the style and have to pay a one time cost of 7 DP.
To learn a Paired Dagger Kata, the character would have to have 5 ranks in the style and pay a one time cost of 14 DP (and no, it doesn't matter if he already has the single Dagger Kata or not, the cost is still 14 DP).
If Ejvyn wants to learn a Two Weapon Kata (2 separate attacks) with Daggers as both weapons, then he needs 5 ranks in the style and has to pay a one time cost of 14 DP.
Every kata that is NOT part of the original style has to be purchased separately using Development Points.
Every kata that IS part of the original style raises the DP cost of the style itself.
Every style that includes multiple weapons (for Paired Weapon Kata or Two Weapon Kata), requires that both weapons be paid for at the time that the kata is purchased (outside the original style) even if one or both of the weapons belongs to another kata.
Is that clearer?