First, in the context of your reference to cultural context, one aspect of your question appears to be whether or not a person who has never had experiences of triangles before can have a triangle experience. Second, it is of interest whether that experience can be brought about by a configuration of shapes which is considered appropriate to elicit the perception of illusory contour.
As to the second question, you seem readily inclined to take the view that someone who has previously seen triangles, knows what triangles are, and can also verbally express that experience (»I'm seeing a triangle!«), can indeed have a triangle experience when looking at the Kanizsa figure. (This is not to be taken for granted. Taking a gestaltist view however will grant that perception at least some kind of actual reality. Consider the question whether you see a second triangle constituted by black lines behind the ›illusory‹ one.)
Now, if we are willing to allow this, then we can actually reduce the whole question to the first part. A common psychological stance on perception, taking input from philosophy of mind, assumes a perceptual episode to be constituted by an object providing stimulation to the senses, leading to a ›perception‹ that is not conscious, which is then somehow translated into a conscious perception that corresponds to a phenomenon, which again is fully recognized in the sense of a perceptual judgement. Here, of particular interest is the difference between perceptual experience and perceptual judgement (you might also ask yourself whether a cat can see a triangle):
[W]e must be careful to distinguish such a perceptual judgement from a perceptual experience. A person may have a perceptual experience of seeing a table to be rectangular without necessarily being willing, or even able, to form the perceptual judgement that he sees that a certain table is rectangular. […] [T]he person may be unable to form the perceptual judgement in question because he lacks the requisite concepts. Thus, for example, one might be prepared to attribute a young child a perceptual experience of seeing a table to be rectangular and yet doubt whether the child is capable of forming the perceptual judgement that it sees that a certain table is rectangular […]. (Lowe 2000, pp. 132–133)
Summing it up, the answer is yes, that person could justifiably be said to see a triangle, however, depending on particulars of the question, the answer might differ.
Taking a different approach, we can take the question to mean: Given which previous experience are we capable to perceive illusory contour?, and there is evidence that the visual system's capability to recognize simple shapes is largely innate (notwithstanding the fact that lack of any visual input will prevent vision to develop in the first place). See Christiaans answer for some more detail. A particularly interesting question in this context, which relates to the difference between perceptual experience and perceptual judgement discussed above, is at what age is a person capable of perceiving illusory countours? In this regard, Ghim (1990) concludes that »infants as young as 3 months of age are able to perceive subjective contours«, and in a related study, Curran et al. (1999) conclude that »by 2 months of age, the infant's visual system contains the nonlinear mechanisms necessary to extract an illusory contour from aligned terminators«.
- W Curran, OJ Braddick, J Atkinson, J Wattam-Bell, R Andrew. 1999. Development of illusory-contour perception in infants. Perception, Vol. 28, pp. 527–538.
- H-R Ghim. 1990. Evidence for perceptual organization in infants: Perception of subjective contours by young infants. Infant Behavior and Development 13(2), pp. 221–248.
- EJ Lowe. 2000. An Introduction to the Philosophy of Mind. Cambridge University Press.