Sadly it will have drowned.
A lot of old wives' tales exist about spiders - the most popular being that they come into the house up drains and bath and sink plug holes.
They don't - they couldn't get past the 'S' bend water in a waste pipe, but in any case, spiders are far too fastidious to go anywhere near dirty drain pipes.
They travel about the house largely unseen, except when they mistakenly walk on path, basin, sink or toilet surfaces, from which they cannot climb out - and that's when you find them - hence the notion that they have come up plugholes.
House spiders shouls dimply be put on a wall or carpet to continue their progress.
Putting a house spider outside will probably cause it's death, unless it can get back intot the house fairly quickly.
House spiders are a particular species, they are born in houss, and are used to warm conditions, and very little water. Outside, they do not adapt, and usually die.
So if you can liberate a spider in your home, do so, they eat many disease-carrying flies, and don't bother you if you leave them alone.