Not exactly. The US military helps fuel our economy because it is used to support business interests around the world, but that's not the reason the Dollar is the world reserve currency.
When Nixon took the US off the gold standard, he made a deal with Saudi to only accept the dollar for oil. In turn, the US would always support the house of Saud.
When the petro-dollar dies, our currency will collapse (probably). Saudi is currently in talks to accept Yuan for oil, at this very minute, as a warning to Washington.