Absolutely. If we start with the human vocal tract as a base, without the tongue one could still pronounce voiced and unvoiced bilabial and labiodental trills, taps, fricatives, plain and aspirated plosives, affricates, nasals, and clicks; as well as velar/uvular fricatives, plosives, and nasals. That's at least 40 distinct consonants, probably more. And in the vowel space, you still have rounded vs. unrounded, and modal vs. creaky vs. breathy voice distinctions. That's a weird phonetic inventory, but in terms of size it's very middle-of-the-road for human languages.
A tongue is useful for modulating the airstream, but clearly even human anatomy has several other ways of doing that. So, to produce complex sounds with completely non-human anatomy, you don't specifically need a tongue; you just a collection of ways to modulate the airstream, which may or may not include anything recognizable as a tongue in the vocal tract. Birds, although they do have tongues, can do a whole lot with just a syrinx, for example. And if you had a creature with, say, multiple spiracles for breathing, one could easily imagine using sphincter muscles to produce different timbres, and multiple overlayed phonations from different spiracles simultaneously to produce a wide range of distinct phonemes usable for language.
And if you want to go even farther afield, you don't even necessarily need a vibrating air column to produce sounds usable for language. Consider, e.g., crickets, which produce a variety of noises through a more violin-like (or perhaps "musical saw"-like) mechanism, by drawing different body parts across each other to induce vibration. Actual crickets don't have a huge variety of sounds that are produced within a single species, but just as a violin can produce different sounds depending on exactly how the bow is drawn, which string it is drawn over, the tension of the strings, and whether you actually draw the bow at all vs. plucking the strings or slapping the body, it is not hard to imagine a creature which produces a range of distinct percussive and fricative noises by the interaction of external body parts equal in size to typical human phonological inventories. As a proof of concept, see this video, in which (among other things) the CODA (child of deaf adults) presenter demonstrates how you can in fact hear sign language. No tongue required.