There is an explicit answer in the Rules--Rule 17, bullet 3, "The robot may pass in/out/through Base, and if you don’t touch/influence it, you don’t have to restart it."
We can also use this as a good example of how to look at the Robot Game rules, since that particular information is already contained in the rest of the rules.
First, and most important:
Rule 3, Interpretation, bullet 3 "If a detail isn’t mentioned, then it doesn’t matter."
Check the Rules--are there any rules that say that a robot has to stop and restart?
Rule 17, Autonomous <> Dead Robot, says that whenever the team touches or influences the robot, then the robot becomes Dead, and must be brought to Base for a restart.
Rule 26, Touching the Autonomous Robot, also says that if the team touches the robot, or anything it is moving or using, then the robot must be brought to Base for a restart.
Rule 36, Interference, notes that if two robots become entangled, then they may restart without penalty.
Rule 31, Touch Penalty, Exception 2, says that you may turn the robot off once when you are done with the match, without a penalty, and without requiring a return to Base or a restart. By Rule 43, Precedence/Authority, this exception overrides Rules 17 and 26
Plus we have a rule that says that the robot can go in any direction until the next touch:
Rule 30, bullet 4, "Once autonomous, the robot can go and/or extend in any direction until the next touch and restart."
Do the Rules say anything about the robot and Base that require a restart?
Rule 30, Starting Procedure, "If the robot enters and leaves Base with no interruption or influence from you, this is not considered a restart, so starting procedure doesn't apply." [this connects to the answer from Rule 17]
Rule 31, Touch Penalty, only discusses what happens after a touch, if the Robot or its Cargo is completely outside Base.
So there's nothing in the Rules that requires a restart.
Do any of the Mission require a restart?
None of the missions mention Base, or a restart. The Obstacles mission does permit penalty-free rescues of the robot. A "Rescue" isn't defined in the Rules, so we use the literal meaning (because of Rule 3, bullet 1) that the team rescues/influences the robot, and it gets brought back to Base for a restart.
What about the Game Updates?
The Updates talk a lot about the Obstacles mission, but otherwise they don't mention Base, rescuing the robot, or restarting the robot.
So, in our analysis, nowhere in the Robot Game documents does it require that the robot stop just because it enters Base. That's enough for FLL--if that detail isn't mentioned then it doesn't matter.
But we also have several rules that say that the robot may keep moving anywhere on the field until it or its Cargo is touched. So that reemphasizes that it is the touch or influence by the team that makes it necessary for the robot to stop and be restarted.