The passage has very loose ties to the reality of the Arian controversy in the fourth century. Certainly there was no persecution of the Catholics at the time, and Felix (II) was not killed. Ursacius and Valens indeed played an important role in the controversy, but they were Illyrian bishops, and not Roman presbyters.
The council of "priests" ("sacerdotes") imagined in the passage would have consisted of presbyters rather than bishops.
As far as the Arian persecutions (imagined by the author of the Liber Pontificalis) go, the Felician abbreviation mentions only "the presbyters and clerics being killed", whereas the Cononian one tells about the Catholic clergy impeded from entering churches and baths (Duchesne 1886: 82). The expression "presbiteri et clerici" suggests that the title of "clerici" is reserved here for the lower clergy.