If I add it to the boil, will it count as alcohol against yeast alcohol tolerance? Would it hurt bottle conditioning if I add it at the same time I add priming sugar?
Short answers No and No.
Although erythritol is an alcohol it does not count against the 'alcohol' tolerance of yeast. When we speak of the alcohol tolerance we are not strictly speaking about all alcohols but Ethanol, Ethyl Alcohol, or drinking alcohol. This is what we refer to when we say yeast is producing alcohol, and what is measured in the ABV on you bottles of alcoholic beverages.
Yeasts do produce other alcohols during fermentation, but usually in such low quantities you don't have to worry about them, unless you are distilling, in which case they can be concentrated to flavour or toxicity thresholds.
Also as this is an Sugar Alcohol, it is not actually a sugar but a polyhydric alcohol, which is not ferementable by yeast. So adding it at boil time or at priming you should be fine.
Just be warned, Erythritol can have a cooling minty flavour, so I would recommend adding it during priming, and prime a number of different bottles with differing amounts, and find your sweet spot (sorry) that way.
Contrary to its name it's not an Alcohol or a Sugar... Wikipedia
I'm pretty sure they won't have any alcohol effect unless it matched a metabolism pathway of yeast.
It doesn't appear to be fermentable. But may have adverse body mouthfeel effects, as it's used to thicken food stuffs.
There are already proven brewing ingredients to get the effect you want. Lactos is unfermentable and used in many beers. I'm seeing Stevia in many commercial beers and ciders.