In general this would have been the case, but there were exceptions. In some cases districts could not supply enough men meaning that men from other districts would be sent to those units. Sometimes units from a certain district would be garrisoned elsewhere. Officers were sometimes transferred between units.
If he was was residing in Regierungsbezirk Koblenz then he likely would have been with one of the units from that city. Since most military records from the period are lost, the only real options for tracing a non-officer would be through casualty lists and other lists (possibly) printed in regimental histories. A complete casualty list (killed as well as wounded/injured/ill) was compiled for the 1870/71 war, partially transcribed at the denkmalprojekt.org . There are Rangliste for officers of the Prussian army, etc. at the Michigan University library, some of which are scanned and online. Link to the 1863-64 volume:http://babel.hathitrust.org/cgi/pt?id=mdp.39015010796087