I don't know that it would bring any tangible benefit to bitcoin specifically, but I think it would bring further legitimacy to digital currencies as a whole, of which bitcoin could potentially be a beneficiary in some capacity, though how much specifically would be hard to gauge.
It'll because non of the new so called digital currency (developed by countries or in development) will have the features posses by bitcoin, her finite supply, decentralized mode of operation etc. The new currency would obviously been in a form of stablecoin that's fix to their local currency, precious metals or US dollars. Also there would hardly be any profit to be made from holding those currency instead it'll mainly be used for purchasing of goods and services and other necessity.
One of the reasons bitcoin is attractive both to the sophisticated investors and everyday individual, is her potential of giving you outrageous gains in the shortest time possible. Her volatile statue is her strength, the government backed digital currency won't be having that therefore bitcoin will still be having a strong advantage over any government backed currency. The competition could be won by them when utilities is been debated on but for the assest aspect, that bitcoin still holds.