If you are talking about a normal country then yes, Bitcoin will co-exist with the fiat national system side by side. Official cryptocurrency exchanges will serve as financial gateways. Citizens investing in Bitcoin will pay taxes levied by the government and fund the budget of the country they live in.

If you are talking about a country which has banned Bitcoin in its jurisdiction, then no. Local BTC holders will be forced to hide themselves in order not to be punished by law enforcement officers. Bitcoin will only try to survive. In any case, the fight against blockchain technology based on a decentralized network is very difficult, so eventually this government is likely to fail.

I consider BTC coins to be investment assets such as stocks which can be traded without involving third parties, so I like the first option. In my opinion, both financial systems should exist, people must pay taxes on their income.