No. The Wii Internet Channel (Opera Browser) uses Flash Player 7/8 (Updated to 9 in later firmware). Poptropica required Flash Player 10+ (later 11+ / AIR).
The Wii browser cannot run Poptropica. It crashes or shows "Plugin Missing".
Flash is Dead. Adobe EOL Dec 2020. Poptropica migrated to Unity/Haxe (Mobile/PC). Wii cannot run it.