If you are sure you'll be in the game exactly once the four timer is ready to play again there is no need to tap them but I'd say it's best you do anyway so you don't get any lag from having them swar...
The count displayed at the end is the number captured in the game. If you make note of the robot parts you have, then add the number from the game you will see how many you got from the other robots. I have had the full 80 added a few times when I had not tapped any for a few hours. I definitely get full credit for all of them in the town after the mini game. Have never got past 52 in the game though.
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