I have a sense of what you're asking, but a strict interpretation of your question leaves me confused. Maybe you or someone else can clarify it?
You see, "look random" and "appear intentional" seem to contradict each other. Both "look" and "appear" are judgment calls. So, strictly speaking, your answer is "no" - at any moment in time, to me, something is going to look random OR appear intentional. It may flip back and forth between the two - one moment looking intentional and the next appearing random. Or, loosening my interpretation of your question some, an object of art may SEEM random and SEEM intentional at the same time - that is, it is ambiguous.
Another interpretation would be this, "Can something be randomly generated yet seem intentional?" Yes. Rorschach inkblots come to mind - generated by random drops of ink on paper which is then folded over and pressed to create a symmetric pattern. Somewhat like art, but our brains are really good an overlaying interpretation and intention on them.
Another interpretation is, "Can something be created with intention yet look random?" A walk through an modern art museum should convince you of an answer to this one: yes. Since the intention is in the head of the creator of the art object and it might not come through in the work of art, the viewer may just see randomness.
And, for completeness, something can be intentionally random. Computer generated "art," if truly random, takes a bit of intentional effort on the part of the programmer to ensure the randomness.