No, mods and plugins used in Studio are not usually used in game. The error messages you see on loading are due to 2 possible causes:
1- The mod your cards is referencing is really missing after the update (you can search it in the old repack and copy it to the new installation).
2- The mod isn't really missing but was updated to a new version. Your cards are searching for the old version and throw an error message. In this case you have to readd the updated clothes/accessories manually to the character card.
Well, this is the safest procedure to update the game, don't forget to import even the Housing, coordinate, plugins config files (it saves you from the hassle to set the settings again) and the BetterHScenesOffsetsV2.xml file.
The update procedure whit the launcher, although easy, is not free from potential problems.