Shaun, unless something has changed in the last day or two, you will not get silver from killing crimson dragons with a faction character. However, the good news is that if your faction character dies to one of them, you also don't go into skill loss.
You get faction silver for killing the other invasion monsters and corrupted townsfolk using a faction character. Killing corrupted townsfolk, however, causes some karma loss. And dying to invasion monsters (other than crimson dragons) or corrupted townsfolk while using a faction character will put you in skill loss.
*Caveat: The above information is what I found to be true using TB faction characters. I haven't had a chance to try it on another shard yet with characters in Minax. *
I have read some posts made yesterday or Thursday about being put into skill loss if you use a faction character for trick or treating and die in the process. The posts I saw seemed to imply this happened in Luna, so it would seem the NPCs that did the killing were not corrupted. Also, there were posts indicating that faction characters that were killed trick or treating were lootable by the public; however that might have happened because the character was in the thieves' guild.