The wiring connector to the ABS module being unplugged should have NO effect on engine running according to what I see on the wiring diagrams.
Only way to find out for sure is to unplug it.

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Supporting Vendor and Moderator of LOST
05 Jeep Liberty CRD Limited
Ironman Springs/Bilstein/Shocks
Yeti StgIV Hot Tune
Week's BatteryTray
No FCV/EGR
Samcos/ProVent
SunCoast/Transgo
Carter Intank-pmp
2mic.Sec.Fuel Filter
Flowmaster/NO CAT
V6Airbox/noVH
GM11 Bld.fan/HDClutch
IronrockArms/wwdieselMount
98 Dodge Cummins 24 Valve

So on the maiden voyage after the lift pump install, I had the wife with me, we both heard a squeak while turning to the right, and loading up the bearing on the left side, so like my other CRD I used to own, same problem was trouble shot, and repaired the same way. I found a good deal on Moogs on Ebay, seller has 2, but both are left side, the only difference is the orientation of the wire, I am sure the ABS trigger will work just fine, so should I pull the trigger, and get them both? Already ordered 1.

https://www.ebay.com/itm/163196140848

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20 year owner of Libby CRD!
2006 LTD Bright Silver loaded with all the needed mods, CCV intact.
Equipped with HDS thermostat, plenty of heat, faster warm-ups, increased fuel mileage.