On your Volvo there are shocks on the rear axle and a strut assembly on the front. On the rear the shocks are simply exchanged for new units. On the front the strut assembly is disassembled and new cartridges are installed and then reassembled (the rear requires a larger array of tools, procedures, and time). If your shocks and struts need replacement it will effect the ride as you have noted, but it will also effect handling during unscheduled emergency moves by the driver such as abrupt lane changes, swerves to avoid debris in the road, etc. I wouldn't think it would cause undue damage to the rest of the suspension system over the short term. Poor suspension condition has rolled over many cars as well as having littered the ditches after excessive body roll has put a car into an uncontrolable skid. Keep your speed down and drive carefully- and replace the shocks and stuts at your earliest convienience.

Randy