Does Tianna stop Conquer and Hold effects?

No, Tianna Crownguard does not stop Conquer or Hold effects from triggering.

According to RiftJudge FAQ 8403 and the sequence clarified in FAQ 9179, Tianna’s ability ("While I'm at a battlefield, opponents can't gain points") is specifically limited to preventing the gain of Victory Points.

The mechanics of "Scoring" (which triggers your Conquer and Hold abilities) and "Gaining Points" are treated as distinct parts of the same process. Even if Tianna prevents you from actually gaining the point:

• The battlefield is still considered to have been "Scored" for that turn.
• Your Conquer and Hold triggered abilities will still trigger and be placed on the chain normally, provided their other conditions are met.