OK Matt...your math is correct the one thing you arn't thinking about is where the center of gravity of your robot is going to be at that point. your arm will definitely be able to support your tetras when your robot it lying on it's side...
assuming that the arm is extended 3 ft up and 4 ft out with a relative weight on it of 150 lbs ( perpendicular distance of 5 ft with 3 tetras on it)
even if the previous center of gravity was sitting on the ground the normal force of your robot would be unable to counteract the weight.
now this is assuming no counter actions, it is possible to make counter forces with springs, and shifting weight but i would still be cautious of doing so because of the amount of energy that would be stored. (for examples of this check out team 47's bot from 2003)