I would drill the holes if your pot is bigger than 2 gallons and if you plan to flower in those pots. If you plan on transplanting before flowering, just wait until then. A few weeks without drainage won't kill them. I would let your root ball fill out that pot before transplanting unless it's huge.
However....: Without drain holes, you can essentially never flush. Yes you can feed it straight water, but sediments and precipitates form from organic and inorganic nutrients. Chemical reactions in your root zone are taking place constantly, leaving behind salts. These salts need to exit the pot in some fashion; ie the bottom of the pot.
That being said, aeration is another thing you are missing out on due to no drain holes.
Don't be afraid to transplant unless you are in the middle of flower. If you are in the middle of flower, you should drill holes. You really won't hurt the roots if your pot is bigger than 3 gallons. Just don't drill too deep or too wide (she-said joke here). Many small holes is the key in the side AND bottom for maximum oxygen as well as drainage.
Your plant probably won't die if you don't poke drain holes, but the quality and yield will be worth the drain holes if you use them.
Another option is to completely remove the bottom carefully from the pot and place it into a larger pot. Ruins your old pot though, and still may damage root ball as much as transplanting.
