I wouldn't worry too much about the teak 'just rotting away' because its natural oils preserve itself quite well. The longer you let it sit before you get around to bringing it back to prime condition will make a huge difference in how successful you are in that task. Unless you clean, sand and
varnish now, or cover it completely from all the elements, mold will set in (that's the silver stuff which affects exposed wood). The more mold that sets in the deeper into the grains it will go and the harder it will be to get out. All the books about cleaning with bleach or oxalic acid don't relay how hard it really is. If mold sets in deep it is probably there to stay unless you physically remove it by sanding a lot of the teak away. Oiling helps replace some of the teak's natural oil it loses through exposure to the elements, but it doesn't keep away the mold. Oiled wood eventually turns silver, too. Either
varnish now or soon, otherwise, your boat will look like mine: a beautiful salty silver.