Running conditioning packs from non turbine type HP ground carts (ie deisel units) is not recommended (at my airline).
The reason is one of potential/possible oil vapour contamination of the pheumatic ducting - the air supplied must be "clean". If oil/vapours do enter via a ground start unit used to power the packs, then they will quickly pass these vapours/odurs/smoke to the cabin, contaminating the LP side.
Using these units to start engines should always be accompanied with ensuring the packs are off to prevent this air from passing through the ACM units.
Turbine (APU type) ground air units are much more reliable deliverers of "clean" HP air - we don;t use these to run packs either for 2 reasons.
1/ They are expensive to use - as we use 3rd party units
2/ They have limited run times due to their fuel usage.
Ground conditioning carts (which deliver cold air) plug into the LP side (usually into the mixer) but are not that effective on widebody aircraft.