Every single day counts, and that applies from the very first day of custody regardless of where that custody takes place.
In Missouri, as in virtually every other state, time served in county jail while awaiting arraignment, trial, or sentencing is credited against whatever sentence the judge ultimately imposes. The clock starts the moment someone is booked and does not stop regardless of which facility is holding them. County jail, city jail, a holding facility, it all counts the same way toward the final sentence.
Even a partial day matters. If someone is arrested, arraigned, and released the same day, that still registers as one day of incarceration credited toward any future sentence in the same case.
This credit does not happen automatically in every case without documentation. The defense attorney is responsible for ensuring the court accurately calculates and applies the jail time credit at sentencing. If your person has been sitting in county for any significant period, make sure their attorney has an accurate count of every day served and that it is reflected in the sentencing paperwork. Errors in jail time credit calculations do happen, and catching them at sentencing is far easier than trying to correct them after the fact through the Missouri DOC.
Once the sentence is imposed and your person transfers to a DOC facility, the time already served is deducted from the total. What remains is what they actually have left to serve, and the county time is essentially money already in the bank.