Q:

How important is it to delete disk partitions when wiping devices?

The command lsblk returns the following output that lists 4 partitions.
sda      8:0    0 931.5G  0 disk 
├─sda1   8:1    0     8M  0 part 
├─sda2   8:2    0    40G  0 part /
├─sda3   8:3    0 883.8G  0 part /home
└─sda4   8:4    0   7.7G  0 part [SWAP]

When executing one or more of the following commands, is the necessary to delete the partitions prior?
If no, why and if yes, why? 
If partitions are not deleted prior to the commands below being run, what is the risk of data remanence?
When executing one or more of the commands below, the partitions are not deleted. 
dd if=/dev/urandom of=/dev/sda bs=2MB conv=fsync
hdparm --user-master u --security-erase password /dev/sda
pv /dev/urandom > /dev/sda

A:

What you are seeing is a cached view of the previous partitions.
If they appear to persist even after a wipe, this is a result of the kernel caching the last known partition table in memory. It does this because it does not expect the layout to change at runtime, so rather than re-read the table each time the partition layout is queried, it reads it once at boot. If you want to force it to re-read the partition table, you can run a command like partprobe, reconnect the drive, or reboot.
The partitioning information is contained in the partition table, which is a small (64 bytes) section of the drive that specifies the location, type, and length of each partition. MBR partitions keep this table at the very beginning of the drive. GPT partitions keep an additional backup at the end of the drive and add support for more features. When you overwrite an entire block device, the partition table is also wiped.

As another answer mentions, the partition layout itself is unimportant and contains no sensitive data. They contain essentially nothing other than the bare minimum of information required to split a disk up into multiple partitions. You can see exactly what is stored for both MBR and GPT tables:

https://en.wikipedia.org/wiki/Master_boot_record#PTE
https://en.wikipedia.org/wiki/GUID_Partition_Table#Partition_table_header_(LBA_1)

