Yes, the holes are vital. You can drill them in some containers, or you can nest a pot with holes inside the other container (removing it when necessary to water). During active growth, your Echeverias will enjoy it when the soil goes fully moist (to saturation) and then has a chance to dry out most or all of the way before they get water again. Without holes, there's no way to flush, so salt will build up in the container over time.
The plants may look cute in a little teacup or whatever, but if you're interested in their long-term survival then find a way to water them well, so that water exits the bottom of the container. And use an airy, quick-draining mix so that it dries out relatively fast afterwards, which helps with the watering and reduces the risk of rot. In our mild climate, given this care and a lot of light, I do not have rot problems with my Echeverias.