[LIST=1]
*]Assuming that a robot is touching its colored tile, can scoring objects be rapidly placed into the robot during autonomous?
*]If so, how many game objects can one member of an alliance place into their robot for scoring during autonomous?
[/LIST]
So, yes this is legal, as the Autonomous Period is part of the Match.
You would only be limited to the amount of Match Loads available to you. The maximum amount of Match Loads available to an alliance is four (4) Balls and four (4) Barrels. This is seen in the definition of Match Loads, quoted below.