Biggest problem in a car is the high level of background noise obscuring the quiet parts unless the volume is cranked. Best way to reduce the dynamic range of the recording to adapt for that is parallel compression (bottom-up compression), which will increase the level of the quiet parts without effecting the dynamics of the loud parts or peaks. The quiet stuff is made audible over the road noise while the louder stuff isn't made any louder than it was previously. The details are brought up while the liveliness of the peaks remain unsquashed.
That approach will sound far more natural and engaging than attempting to squash the peaks down with limiting / top-down compression enough to achieve a similar reduction in dynamic range.
The need for doing more than that will depend on the recording. An AUD recording of the PA sound will already be effectively limited at the top-end without extraneous peaks, unless the audience reaction is louder than the music. When the audience is louder than the music, or if the recording was made at the stage-lip or on-stage where the dynamics of things like the drum kit are significantly wider with far bigger peaks, it can help to do a bit of limiting to manage the handful of highest/wildest peaks first, then normalize, since those errant peaks will tend to drive average levels down significantly. On its own, limiting those peaks won't make it sound better, but will provide room for the normalization and the parallel compression to bring up the average level and the lower level parts. If trying to do it using limiting/top-down compression alone, its going to be difficult to get it sounding transparent given the amount of dynamic range reduction required.
But if you want to do the best you can, using a combination of dynamic reduction techniques like that is a good idea, as it will make the most of the bottom-up / parallel compression. But almost all the audible improvement will be from the bottom-up part. Just be aware that bottom-up / parallel-compression is going to increase level of all the quieter elements, good and bad, which includes the ambient noise floor, audience chatter, etc.