It uses end of season rank for rewards, so you can drop during preseason and it won't matter, but not before the season ends.
It's extremely difficult to drop tiers however so I wouldn't worry too much about losing streaks causing you to have a tier demotion. You'd need to be playing at a gold 5 level to demote from plat 5 to gold 1, so if you have any business whatsoever being plat than you should be fine.
(Also note that end of season ranked rewards have not been announced yet, so may not include a border. Next season they are currently planning on showing a border that displays you current rank during that season split (as opposed to previous season border), so there will probably be something other than a border as an end of season reward this season.)