This is exactly what you’re thinking it is: the antonym (i.e. the opposite) of ‘regurgitate’. So it means to swallow something greedily (which my mum tells my dad off for doing with crisps). You can also use it figuratively – so you can ingurgitate a good book, for example.
You used to be able to just ‘gurgitate’ as well, although that means the same thing and seems to have fallen out of use completely (and isn’t to be confused with ‘gurgitation’, which means ‘a boiling or surging of a liquid’ (from Merriam-Webster)).
Ingurgitate was first seen way back in 1570. And whether you’re in or regurgitating (and I think we can all agree that the former is probably preferable, although might lead to the latter if you do it too fast), the etymology is the same. Both come from the Latin word gurges which means ‘whirlpool’. Although the link might not seem immediately obvious, it’s probably down to the action of whirlpools engulfing things which brought us to ‘gurgitate’.
(Bonus fact: The biggest whirlpool in the world – technically known as a ‘maelstrom’, which is an awesome word – is called the Saltstraumen, and is just off the coast of Norway, near the Arctic Circle. It forms four times a day as tides carry huge amounts of water through a small channel that’s only 490 feet (150 meters) wide. It’s so big that boats have to make sure they travel through this stretch of water when the maelstrom isn’t active.)