The answer to "if we could see ultraviolet light, what would it look like?" rather depends on exactly in what sense we could see it.
If the the range of our eyes cones were extended such that one or more types of cones could receive partially in the ultraviolet range (and the sensitivity within other ranges were modified such that we could resolve ultraviolet light in isolation), then UV would look like our current limit of purple.
If we had another type of cone in the eye explicitly for this range then we'd probably see UV as another primary colour. And describing it as a deep purple would be like describing red as a deep green.
If we had more than one extra type of cone, we'd probably have more than one extra primary colour.
Of course beneath all this is the philosophical issue of how we can know whether we're seeing the same colour, and how we could ever even begin to describe the phenomenal experience of colour using words