It can work both ways and I've seen it. This mostly occurs if a body of elders recommends someone that for whatever reason, the CO doesn't want to approve. If that happens, and they don't work this out at the elders meeting with the CO, than the CO will forward his letter as to why he doesn't approve of the appointment, along with the elders explaining why they disagre with the CO, along with the summary on the CO's report. In almost all cases, the Service Dept will side with the CO.
In some cases, an elder moves from another congregation and the appointment is held up. If the CO likes the former elder, and there is no "organizational" reason that has been violated, then he will be appointed, even if the new congregation elders don't want it.
There are some "problem" brothers (whom I've since come to learn, have a soul and a mind that they haven't quite wholesaled out to the Borg) whom don't get along with the elders very well, and are always in the CO's ear. Whether they be MS or not, typically, the CO has to ultimately make a call as to whom he will support. If the BOE has a good reputation, the complaining brother will always lose. If for whatever reason, the BOE and their congregation isn't doing good, and the brother can make a good argument, his chances of getting approved do go up.
It is very situational. Bottom line, it is the exception and not the rule when both the BOE and CO do not agree, and yes, a huge portion of that reason is the politics involved.