Typically yes. Mating lowering springs to OEM struts is a No-Go and will cause the OEM struts to wear out prematurely, particularly if the vehicle is lowered more than 1" on OEM struts; and in most cases affects the ride quality of the vehicle too---generally, making the vehicle have a bouncy ride. You're better off lowering your car right from the get-go by installing a quality set of coilovers, or aftermarket lowering spring/strut combo. Air suspension is another option to consider, albeit an expensive one.
There are folks on the forum who've lowered their coupes using Eibach springs along with OEM struts and said the ride quality wasn't compromised significantly. You may want to search the forum and follow-up with them to see if they experienced any premature strut failure.
