My understanding is: they won't have to since the WBC CBP is only for those who are current champs, currently ranked, or something that the WBC mandated.
They don't mention anything about unifications from a WBO or IBF champ.
In your example however, if you're the WBA champ, unifying against a WBC champ, you're already under similar testing protocol.
Each of the following shall be considered or become an Eligible Boxer subject to testing under
the CBP:
1. Any boxer who as of January 1 of each year is a WBC World Champion;
2. Any boxer who as of January 1 of each year is ranked in the top 15 in the WBC
World Ratings or who throughout the year becomes ranked in the top 15 in the
WBC World Ratings;
3. Any boxer who becomes eligible to challenge for a WBC World Championship
bout through a WBC ruling; or
4. Any boxer who does not fall within conditions 1-3 above but who voluntarily
submits to become an Eligible Boxer under these protocols
the CBP:
1. Any boxer who as of January 1 of each year is a WBC World Champion;
2. Any boxer who as of January 1 of each year is ranked in the top 15 in the WBC
World Ratings or who throughout the year becomes ranked in the top 15 in the
WBC World Ratings;
3. Any boxer who becomes eligible to challenge for a WBC World Championship
bout through a WBC ruling; or
4. Any boxer who does not fall within conditions 1-3 above but who voluntarily
submits to become an Eligible Boxer under these protocols
In your example however, if you're the WBA champ, unifying against a WBC champ, you're already under similar testing protocol.

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