definitely. i have my regular-sized pots set up on a timed drip system so they don't get a big flood of water all at once. i think this is a one of the reasons why i've almost never had runoff coming out the bottom. i keep a measure on the amount of water given to each single plant and the plants never suffered from any moisture stress. i watered for one minute at 11 am everyday.
in this case, those holes on the bottom of the pots probably didn't serve any drainage purposes, however, i'd strongly encourage you to make sure you have some holes in the bottom of your pots/cups/whatevers. with the party cups, it was actually super easy... i just flipped them upside down, took my Bic lighter and put the flame to the bottom of the cup (cup's upside down, the flame is above the cup but still touches the plastic) and as soon as it started to burn through, i backed the flame off. makes fairly round holes, there's no mess if you don't eff it up and burn it too long, and it's just nicer. i've only done that with the party cups. i'd say to put the holes on the bottom-most parts of the cup or 20 oz bottle or w/e, cuz you've seen the bottom of some and they're uneven or jagged. putting the holes on the bottom-most part helps ensure the water actually drains out the holes. i always put a hole in the middle as well, just cuz. for that small container, maybe dime-sized or smaller holes will be okay. you don't want your growing medium to come out the bottom though, so use that as a gauge.
not only do the holes allow for water to flow out, keeping the soil from suffocating the roots [since they need oxygen as well as water] but if you have a tray on the bottom to catch the water that comes out (also suggested) then your plant will be able to absorb some of it back when the soil starts drying out a bit. every time you water, the water also pulls down air to the roots, but if the water builds up or has nowhere to go, then i imagine it doesn't pull nearly as much air.
sorry for the long-ass paragraph(s). lol. are you trying to keep them in small containers so you'll have smaller plants, so they'll be less conspicuous? here we get sun on most days, and the rain is like nothing. but i got neighbors and my yard is really exposed. i don't even like to go out for a smoke, it's so not private. one day i'll have my 10 acres of greenhouses, full sunlight, and no damn neighbors. hah. i don't like the uncertainty of the weather though. i'm sure if i grew outdoors, lest a greenhouse, a tornado would come or lightnight would strike my plants or i'd have a rabid monkey rip through them or something. that'd be just my luck..
