CDJ's, Mp3's, true peak overages and CDJ DSP's

This is regarding to how CDJ's (namely the 3000's, and NX2's, as they run in 32 floating point) treat mp3 files with 0dbFS overages.
0dbfs overs are super common in most commerical music mp3's.

There's not much technical information about how the DSPs and DAC's in the CDJ's work, currently, my understanding is that tracks are processed in a 32 float 96khz engine (3000's) before being sent to it's outs, and if using SPDIF(Digital) is spared a DAC->ADC conversion cycle before getting to a DJM's channel DSP.

If SPDIF isn't used, what happens to an mp3 with true peak overs like that?
Is there headroom applied before the DAC conversion to fixed point and sent to the outs so that there's no clipping distortion?
How're these overs handled in a DJM's DSP if SPDIF is used? (not an issue if your gaining normally?)

What brings this all on, is I recently found an mp3 encoder that has clipping protection settings when converting from lossless, so it'll decrease gain to make sure the resulting mp3 doesn't have 0db overages.

But is this even necessary?
Do CDJ's have processes in place to ensure inter-sample distortion doesn't happen in it's DAC's?
Should I not worry that all my mp3's have true peaks over 0dbFS?

Sorry for getting into the weeds with this one. A lot of yall prolly don't care, but any insight is appreciated. Also spare me any "why don't you just use lossless", responses.