Maybe not. Around here most "sump pumps" only remove ground water and storm water.
A pump that moves sanitary sewage is usually referred to as an "ejector pump".
Seems like Ryan has a "clean" water problem and not a "dirty" water problem.
Anyway..........
If it is sanitary sewage you're cleaning up, remove the carpet without question.
If it is storm water or ground water, you could consider cleaning the carpet and saving it. But with young kids, probably replace it just to be safe.

Sorry to see this Ryan.
Batten down the hatches, more rain coming your way.