Can a Warlock research Original spells?

The Dungeon Master’s Guide (Page 198) details how to create your own custom spells by doing in-universe research. It states that “A spellcaster of any kind can create a new spell”. Whether a Warlock is even a spellcaster is already arguable. They don’t technically cast spells, they have invocations. However, they do have caster levels. Meaning that they are, perhaps, spellcasters without spells.

My question: Does a Warlock qualify for researching new spells? And if yes-… Can they actually learn their own spells as an invocation? Or have they made a ‘spell’ that they can therefore never use?