That's not how shiny hunting works. In Crystal, there is a 1/8192 chance for a Pokemon to be shiny. This does not mean that once you hit the 8192 encounter mark, you are guaranteed to get a shiny. You can get it at encounter 1, encounter 5000, encounter 8192, encounter 10000, or whatever encounter imaginable. Each soft reset, your Dratini has the same 1/8192 chance of being shiny. This also applies to future games where the shiny odds are 1/4096 instead of 1/8192.
Furthermore, soft resetting is not a chain. You can close the game any time. In most games, like all Switch titles, you have to close the game to soft reset.
Tldr: closing your emu is perfectly fine.