Not negligible. The amount of excitation a generator gets and these small relative phase angles determine how much power it feeds into the network. Should things go crazy and one generator try to take on more than its share of power (say more than its prime mover can handle) then it will quickly go completely out of synch and the network might try to convert the generator itself to a prime move (a motor). Under these conditions sparks fly and breakers open.
All this is complicated by all these generators being located hundreds or thousands of miles apart. The transmission line is going to impose some phase angle of its own (delay) due to the distance of any point on the transmission line from any of the generators. Each generator gets synched to the network at its own location.