I don't know how much this matters, but does a Geist's Threshold limit what kind of effects death had on him that aren't directly tied to combat? For example, if a character died in a drunk motorcycle accident and was horribly mangled in the process, thus becoming a Forgotten, would he be unable to become drunk as a Sin-Eater, or can only Silents get that sort of effect? Would becoming slightly double-jointed (at least in a way that wouldn't warrant a Merit) be allowed as such a side-effect?
The traits a Sin-Eater takes on in terms of flavor and relation to death tend to reflect how they died, and the specific circumstances override general rules (hence the sidebar discussing how many suicides become the Silent, but not all). If you want to emphasize a certain theme with the "can't get drunk" idea, hey, by all means. If you want to be slightly double jointed (athletics specialty in contortion?), go for it.
My advice would be to think carefully about what you choose to use as your traits. This is your big chance to make visible some of the themes and strengths/flaws of your character and to provoke thought from observers about the nature of his or her death. Is it as big a deal as attitude, one's Geist, et cetera? No, probably not, but it is a series of traits that will affect your character's day to day life. How do they feel about not being able to get drunk? Does the double-jointing give them painful reminders of death, or gleeful exultation that they yet live?
One Last Thing
If your character was drunk driving, why do you feel he's one of the Forgotten? You may want to consider the idea that another Threshold might be better; after all, drunk driving accidents aren't "freak circumstances" so much as "prophetic knowledge of imminent death".