No, I'm not going to get into the whole "rapier spears" thing here. Rather, what I'm going to drop here is a bunch of references to historic unarmored spear.
At one point during a discussion salon at yesterday's event, one person mentioned that there are no examples of unarmored spear use. (In the context of this discussion, "armor" was referring to something along the lines of SCA heavy armored combat, so meaning a historical equivalent of full heavy battlefield armor.) Using heroic amounts of restraint, I didn't say anything other than "you're wrong" and "let me get back to you with references." So here we are. (As an aside, I want to thank the nice people behind Wiktenauer so much. Seriously, this is an awesome resource.)
Firstly, I'd like to bring up our own Don Dylan's research on the London Masters of Defense, and their playing of the prize! Dylan notes that the Morris pike was used in such fights. He also goes on to note that "It is also uncertain if participants wore armor during the prize, but it is reasonable to assume that they wore at least some armor, perhaps a buffcoat." A buffcoat by itself would certainly offer protection against cuts and some impact, but absolutely doesn't approach "armored" in this kind of context.
Along those lines, John Clements has an essay (yeah, I know, Clements) which also notes that the participants playing the prize were unarmored, and made use of the Morris pike.
From there, let's go look at historic manuals!
Fiore has a section on spear. So does Vadi. Trending later, Manciolino covers spears (with and without shields). Even George Silver talks about them.
Fiore and Vadi spend time discussing a lot of battlefield weapons. However, I find it notable that the illustrations used in both their manuals have a very high degree of men in civilian dress demonstrating the techniques - including spear techniques. Fiore goes out of his way to note in his manual that in general, anything that can be done in armor can also be done out of armor. (There are some exceptions - for instance, there are some defenses that you may not want to do without something rigid, or at least padded, on your forearm, but even those are better off being done without armor than getting stabbed.) He takes the time to note when there are techniques he describes that should only be done in armor, which certainly implies that those aside, you can absolutely perform anything else in his manual with or without armor.
Marozzo and Silver are, in my opinion, trending far into the civilian area of combat. Certainly, at that point, it wouldn't be expected that you would be wearing a full harness of plate. Illustrations in Opera Nova bear this out, as well.
In short, yes, there is absolutely more than enough evidence for the historic use of spears in an "unarmored" setting.