Most fittings have the gripper first so once you've cleared that the tube should not blow out. However if the tube isn't fully inserted through the internal o-ring then it'll generally leak immediately.
If the tube is scratched on the outer wall, by say dragging along the floor, then there is little chance of the o-ring managing to give a perfect seal. You then run the risk of "slow" leaks, either immediately or at some future date.
Most, if not all, fittings have a mark on their outer body to indicate the depth of insertion required. Fitting instructions generally state that you mark the tube with a pencil in accordance with this mark and then insert until the pencil mark aligns with the end of the fitting. It's a simple quality assurance measure that you ignore at your peril.
Full insertion also helps support the tube within the fitting from distortion due to any side-pull forces that the tube and fitting may be exposed to. Such side pulls can encourage leaking.
Inserts are also essential to ensure the tube is prevented from collapsing and so negating the work of the 0-ring seal.