Actually the vape question is a good one, because it is not the nicotine that causes this effect it is actually polycyclic aromatic hydrocarbons (PAH) and other tar-like compounds in tobacco smoke that increase the activity of liver enzymes thus decreasing the effectiveness of many benzos. For example: (dip, chew, snus, gum, patches, etc...) do not have any kind of effect on benzos. So the question remains do e-cigs produce PAHs? And if they do at what level?
I would imagine the higher the temp at which the e-juice burns the higher the likelihood that it would produce PAHs. I would imagine drip tanks with mechanical mods or box mods set to 100+ watts would have a higher likelihood of doing this than say someone using a subtank or atlantis on a sub-ohm setup.
Not a whole lot of studies have been done on e-cigs so I do not know if they emit PAHs or not. If they do, it will effect it. If not then you are good to go.
edit: actually I just found this
http://ehp.niehs.nih.gov/122-a244/
So, I guess it is possible but the studies do not mention the specifics, AKA: wattage, juice used, temp, coil setup, etc.