You need to be more precise with your terms.
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.
But while I could imagine a bitcoin-like currency acting as a reserve currency I don't see why the organisations involved would not just start their own blockchain and impose their own restrictions on who can participate in the network. I can see a continued future for todays Bitcoins continuing as an almost unregulated grey market currency, but find it difficult to imagine them going into mainstream use in its current form.
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.
I mean the IMF could replace the SDR basket of currencies with "govcoins". It would require an international agreement along the lines of Bretton Woods (probably involving the G20) where countries agree to a specific exchange rate against govcoins, and to hold a particular quantity as reserves. IMF have already floated the idea of replacing USD with SDR as a global reserve currency, the transparency a system like bitcoin could provide might make them more acceptable to some countries.
Thinking about it the main advantage for governments of adopting bitcoins rather than starting their own equivalent would be the amount of work in developing a sufficient pool of coins. Would it be cheaper for them to start mining from scratch or to buy out a sufficient quantity of bitcoins on the market? The fact that bitcoins already have a perceived value would favour their use, on the other hand they may not be keen on rewarding the current bitcoin holders.