When I use Imakuni?'s Doduo's "Frenzied Escape" Pokemon Power, can I put the card into a top-loader to prevent it from getting damaged when I throw it?
No, that would cause a "marked card" situation and is not allowed. Besides, you could really hurt someone flinging a top-loader like that (shame, shame)!
Source: Evolutions FAQ (2016-11-03), TPCi Rules Team (2016-11-03)

Relevant cards

Note: All applicable cards may not be listed below.
XY12_112