Quick Answer
Relationships can help you get noticed before a contract is competed, but they won't decide who wins it. Once a solicitation is out, federal agencies have to score every proposal against the exact criteria they published in that document. So the strongest proposal usually beats the strongest relationship, not the other way around. The practical move is to build visibility and connections before a solicitation drops, then win the actual competition with a proposal built around exactly what the agency said it would judge.