My front sway bar links are going out and causeing a popping sound ALL the time, Some people incuding a Volvo shop foreman said the car is drivable without the sway bar, is this true and how will it be any different with or without the sway bar connected?

The car is driveable without the swaybar, but stability on the highway and curves will not be so good. It's not hard to replace swaybar links.