Yes it can, but minimum supported is 4x, not less.I have both the NEC 3500A and the Lite-On 5328S. I am displeased by the fact that the NEC does not burn at a speed of 4x, because I often need to burn CDs at this speed, so that some copy protected CDs are properly "cloned".
In your current situation I don't think that burning at 4x will improove the performance with your car audio recorder. I think you should rather try different media, until you find one that your car audio player likes. Of course, the Lite On CD-RW burns CDs better than the NEC 3500A, so you might see some difference if you get it, thought I dought that burning at 4x will be the solution to your issue.