There's no evidence to back up this assertion. Many economies that don't have reserve currency status do just fine (e.g. Switzerland, Norway, S.Korea). The expense of US overseas deployments far outweighs the benefit of having a militarily enforced reserve currency.
You're missing one key difference: Switzerland never had the overseas garrisons to start with. For the US not to, it will have to withdraw from them. That will be seen as a sign of underlying weakness. The strength of any currency is relative to the confidence that the government that operates it will continue to do what it does.
There's precedent: look at GBP as the UK dismantled its empire.
