on a personal note, i do not think governments invest in bitcoins secretly because it's a decentralized peer to peer transaction with no central authority and also it can affect the country's fiscal policy, business and also help to facilitate crime rates.
The government are too smart and i dont think they will invest in bitcoin because its decentralizes and they will not benefit from it.
Invest? I think they would invest in such thing since it is profitable in the long run. In terms of the government not accepting it in their country, that is possible since there are some instances that it may affect their country. We can't say that the government don't invest on cryptos since there are some politicians that know and invest some of their money unto Bitcoin and other cryto currencies. If they are too smart, they should know the positive results Bitcoin may bring in their country but they don't.
Yes, everyone can invest in bitcoin without having to publish it, about the legality or not of bitcoin in their country, I think that is something that can be ruled out if they have seen the benefits and also the potential of bitcoin. Therefore I have personally seen some famous people who can be said to be public figures who invest in bitcoin, so it does not rule out the possibility if a government also investing in bitcoin.