Yes, when you select "Erase disk and install Ubuntu", that does delete all partitions on the disk, even encrypted partitions. However...
Deleting partitions does not mean erasing all data! Yes, after you delete the partitions, the data will be harder to access. But the only way to really get rid of sensitive data is to overwrite it and make sure it's overwritten. I like to use the
shred command on hard disks which I want to eliminate data on.
If you really, really want to get rid of data on the hard disk, first find out the device name of the hard disk itself (usually
/dev/sda on a laptop with no other internal hard disk drives and no SSDs). GParted can be useful for such a task, or you can go partway through the installer and it'll tell you what the device is, then back out of the installer.
When you're sure you've got the correct device, and you're sure you are willing to lose all data stored on that drive, you can use the command:
shred -vz [device]
This will wipe over the hard disk with random data three times, and then write zeroes to the drive so that applications will not complain about random data on the disk. The
-v option will tell you the progress of the disk wipe, too.
Please note that this process can be time-consuming; depending on the age of the disk and its size, this process could be done in 15 minutes or it could take hours. Based on the impression I'm getting of the rough age of the laptop, I'd guess it takes about two hours to complete.
If you need the process to take less time, and you don't need three-letter-agency-grade data disposal , then you can tell
shred to make fewer passes with random data (or not to bother zeroing the disk afterward, since in my experience that's not strictly necessary):
shred -vn 1 [device]
This will overwrite the disk with random data only once (instead of three times), and will not zero the disk. This should take between 20-30 minutes to complete. If you want zeroing too, add the lowercase letter
z between the
v and the
I hope I didn't overwhelm you with information.