You should always run a full upgrade when installing a new package to make sure your versions are all in sync. Like if your new package is looking for version 1.1 and you have 1.0 installed, the new package won’t work. In general, everything should be installed with ‘pacman -Syu’ not just ‘pacman -S’

If you don’t install any new packages, then no you don’t need to upgrade anything. You’re just missing out on security patches and upgraded features. It’s worth running occasional upgrades.