As I understand it yes. That line had nothing to do with the atlantic slave trade and everything to do with the barbary one.
At the time that song was written, the Royal Navy did not in fact rule the waves at all (we were latecomers to the colonial game relatively speaking). It was a song designed to exhort people to the goal of ruling the waves, and so (amongst other things) protecting the UK from pirate raids.
Royal Navy manpower needs vastly exceeded volunteers, so press gangs (impressment into naval service, essentially conscription) was used. If someone had some sailing experience, for example serving on a merchant vessel, they were liable to be conscripted into the navy.
Conditions on longer voyages were pretty terrible. According to everything I've read, scientific minds figured out scurvy quite some time before the same solution penetrated the skulls of the admiralty. So on long voyages there was potentially a high fatality rate of up to 50%.
My reading of this is that they needed to maintain morale. Barbary Slave raids were a credible threat everyone faced, particularly as if you were likely to be pressed (by virtue of not being useless on a ship) you were also likely to live near the coast (where there are ships). So even if you weren't particularly bothered about ruling the waves for trading or imperial reasons, preventing slave raids would be something to feel good about.