It will work, until that one time when too much water is added, or, out of fear, you wait too long to add water and lose a plant to desiccation.
Someone above suggested turning it almost upside-down so it can drip out, but I usually just lay them sideways for a few minutes to see if anything drips out. At time time of year, when it's 95 every day, I don't worry. I'm used to how much water to add to them so they're dry again in 2 days.
I have a few pots with no holes and plants have been growing happily in them for years, but I'm aware of the risk and so they are not my only copies of those plants.
Soil that doesn't drain can also accumulate substances from tap water which can make a plant ill, or alter the PH and cause a plant to become unhealthy.
There is a 3rd option - beyond just risk or drilling a hole, that I don't think has been mentioned here, which is to use that pot as a cache pot to hold an inner pot that has holes. You would take the inner pot out of the outer pot to water, let it drip, then replace it back where it was. To find something that fits, you might need to repurpose some plastic item that wasn't made for being a plant pot but happens to fit in your cool pot. Anything you can add holes to will work.
A 4th option could be to rig some kind of wick setup using a gravity system with a reservoir above the pot and wick going from reservoir to pot.
Best luck!
