Uhh.. randomly? At a veterinary? No.
Even if she has an infection and there's swabbed mucous membrane cells sent into a labor, you usually don't have "sperm experts" sitting there on the analysis, not to talk about why they would analyze the shape and form of the sperm for any reason "randomly", if their job would actually be linked to defining an effectively working (destroying) antibiotic medical for the build-up bacteria from an infection, as example.
How long does ejaculate stay in her.. if you go for a walk afterwards, she pees two, three times and walks for half an hour, most will be outside. The movement together with peeing and self-cleaning by licking, the build up wetness getting ejected towards the opening quite quickly.
There are surely small amounts of sperm left, but it is plain impossible to take "an analysis of the whole surface of a female dog's reproductive organs internal mucous membrane" to find remaining sperm for no other good than "to find something to prove you as someone who copulated with this female dog". Hell, the amount of time and work which would go into this.. unbelievable.