Systems such as Target2, CHAPS, Fedwire, etc., exist to allow governments and large companies to settle EUR/GBP/USD transactions in real-time, with finality, on the books of the respective currency's central bank. To that extent, the Bitcoin network can be seen as the Real-Time Gross Settlement system of the Bitcoin currency. But it's important to realise that the currency and the RTGS come as a pair. Target2 for EUR, Bitcoin network for BTC, Fedwire for USD. The concept of a "reserve currency" doesn't come in to it.
(It's also worth pointing out that SWIFT doesn't really come into this discussion - it's just a messaging network..... payments are ultimately settled by the underlying RTGS.)
Fair enough - I'm not that familiar with these topics so any corrections are welcome. The system would act as an RTGS and currency, and would probably run over the SWIFT network rather than the internet.
Following the logic above, then, what do you mean by a reserve currency? Typical definitions encompass the notion that a reserve currency is one that governments hold a lot of, either as an asset or as a way of settling obligations -- and/or the notion that it is a currency in such widespread usage that major commodities are priced relative to it.
In both cases, the currency needs to be widely adopted -- so it's not obvious that a government-bootstrapped currency, with strict usage/membership rules would really take off.