It would seem unlikely.
While the short story Aficionado forms part of the narrative of Existence, that is the only reference to Uplift that we see in any of the book.
All Interstellar travel in Existence is shown as slower than light. Both the Crystal Viruses and the Von Neumann type probe snippet that originated in the short story Lungfish. The Uplift universe has multiple ways to evade the barrier of faster than light travel.
Whilst it is on the surface plausible that Existence takes place before contact in the Uplift universe, given that all the sources of Crystal Viruses believe they have no other way to spread than to use the virus method that would suggest large numbers of species that have reached intelligence and are cut off from the Civilization of the Five Galaxies. Given the reaction of other sentients to the existence of mankind as a wolfling race having dozens of them littered around the place, as well as machine colonists making the same mistake, would seem unlikely