As for archaeological evidence specifically, there's not going to be many surviving battle-damaged sword blades out there, because surviving medieval swords tend to be better-preserved pieces kept in royal armories or the like. In addition, a sword that comes into contact by another sword is not going to damage the blade in a way that is necessarily distinguishable from the numerous other things that a blade could be damaged by on the battlefield.

The larger answer to your point is an unconditional yes. It's a curiously prevalent myth on the internet nowadays that swords were not common and were merely status objects. This is a false interpretation, proved wrong by an overwhelming of art, records, and writing from the period that show swords being used commonly both on and off the battlefield. The idea that swords were rare or especially expensive is a common misinterpretation that seems to come from a conflation of many different time periods into the stereotypical amalgam of "the middle ages." For a 7th century Anglo-Saxon warrior, a sword may have been a precious and expensive item, but for a 13th or 14th century Englishmen, a sword was pretty easily affordable. You can see in both judicial records and literary accounts that enough cheap swords were available for all manner of ruffians, criminals, and ne'er-do-wells to acquire them and cause trouble. An aristocrat's sword would still be an expensive piece, but the arms market had a wide range. By the late medieval period, a sword would probably be one of the cheaper pieces of equipment for the average soldier; he would have to pay much more significant sums for a horse or for armor.