Mine don't.
When I went to pick up the sulcatas at the owners house, the female had a 6 foot tunnel dug in her enclosure. I thought to myself, "what am I getting myself into." as I didn't want a tunnel in my yard.
I have three adults and none of them dig. A lot of times, digging is a way to thermoregulate their temperature or a place to hide.
I have provided them with nice and comfortable temperature regulate places to sleep. So they stay warm enough and have a place they feel is secure for them.
My backyard is also heavily planted, so even in the hot summer days, there is plenty of "cool" spots for them to retreat to when it is hot.
SInce this is provided, they do not need to dig.
I am sure there are tortoises who may dig regardless, but if the necessary steps are taken to prevent it, the chances of digging are greatly reduced.