Humans often breathe through their nose and yet we talk just fine. Fish breathe through their gills and yet make noise through their mouths (underwater, but still relevant). So, the real question is:
How do your cretaures eat?
If they eat solids, then you need to deal with the gagging/coughing reflex to clear the old food tube (and, if I remember my high school physiology class correctly, you also need to deal with pressure equalization). That means lungs (unless you always use vomit, but all that acid wouldn't be evolutionarily sanguine, ifyouknowwhatImean). Where there are lungs, there is the potential for spoken language.
But! If your creatures don't eat solids (for example, nutrients through fluid/skin contact), then you have a problem. To very strictly answer your question, without lungs you cannot have a spoken language. But, if we opt for the more general audible language, then you can click,1 snap, stomp, clap, and fart your way to all kinds of deep philosophy. We humans make sound with all kinds of body parts. And that begs the second real question:
How do your creatures hear?
If your creatures have ears, then any method they use to create sound can be used to create language. If they don't have ears (the ability to detect vibration in a gaseous medium), then this really doesn't matter, because your creatures must be capable of detecting something going on with their associate or the conversation will be very short.
1 When you listen to the aborigine, listen for the mouth noises. The clicks, snaps, slurps, etc.