They can in the Japanese language, at least. Namiko Abe notes that Japanese has a pitch accent, which can sound like a monotone to a new speaker's ear. Do mo A ri ga to, Mis ter Ro bo to. The pitch accent is based on the two relative pitch levels of high and low. Japanese sentences are constructed so that when spoken, the words sound almost like a melody with rising and falling pitches, like a steadily flowing stream. In contrast, English uses a stress accent. We pronounce our accented syllables louder and longer.
I always thought a poem ought to include rhyme. A haiku does not. But it seems to me that the English version ideally would at least include a modicum of meter, obtained by giving each line a distinct meaning and stressing the odd-numbered syllables.
The following English haiku has no rhythm. In fact, the middle line ends with an unstressed preposition.
This is actually one of a large number of unintentional haiku sentences discovered by a bot as it scanned the text of the New York Times in the fall of 2020.
None of them follow my pattern of stresses, and the bot isn't perfect; many of its found sentences don't strictly follow the 5+7+5 rule. But here are 28 that do.