Oh, yes. Digging is the best way to eradicate lesser celandine if you don't want to use herbicides. And herbicides take several years of applications because the tubers are not easily killed.
You should also dig the plants before or while they are in bloom. That keeps them from setting seed. Seeds might linger in the earth from past blooms, but those new plants will dwindle if you keep up on them. That's not to say you are wasting your time to dig after they've bloomed. You'll still be preventing the spread by tuber.
I police my lot yearly looking for new plants. They look a lot like violets, but I can tell the difference. Even the youngest have two or three tubers. Big plants can have 20 or more large tubers.
I'll send photos of violets versus celandine, too.