My experience with dead/dying civs is that one of your dorfs will declare itself monarch as the first spring arrives (i.e. after 1 year). There are claims it can happen at other times, though. Right after embark, you can check the civ screen to see if the monarch still lives.
When playing dead/dying, I generally appoint an engraver out of the summer or autumn immigration waves and starts smoothing stone to build up skill. A monarch suite can also be dug out during the winter and the engraver set to smooth it, while I churn out furniture en masse to build up skill and create masterworks items for installation in the royal suite. The royal rooms are made 11*11 in size, and when eventually engraved and provided with the required furniture of masterworks quality, will satisfy the total quality demands (actually, lower quality will do). I've never had a monarch go grumpy enough to start to punish people for not increasing the room quality fast enough, however (Actually, I've never even seen grumpy thought about inferior quality from the royalty, although I think I've once seen some other noble who had an unhappy though about the inferior quality of his premises).
The major problem royalty causes for me is the incessant string of mandated production, especially if the fetishism is for weapons (which require metal that I typically don't have on my embarks), or RNG stuff such as rings, scepters, etc. where you can't just produce them, but will have to check time and again to see if you've managed to produce enough.
Turtling or not should be based on the embark, in my view. Getting logs for beds is useful, for example, and I am always careful about caverns anyway, since I don't like losses of any kind.