[...some treated wood has cyanide in it. ]
Some old treated wood does, but since that time much of it has been out-lawed.
You may want to check to see if your lumber has any tags on the ends -they would disclose if it contains cyanide of if it uses the newer copper nap. compound.
Copper Nap can be bought as a surface treatment for your boxes (used to surface treat plain pine).
Generally, I don't like the idea of it being where my bees can traffic it into the hive.
This has been discussed in pallet making.
In these situations, the bottom board is treated plywood/dimensional lumber.
State inspectors have told some people as long as it has been weathered, it is ok.
I'm not entirely comfortable with this idea because I have seen treated lumber swell in good rains.
This means that the chemicals (though assumed safe) could leach out into this surface water.
If you paint the bottom board, it eliminates the absorption of excess water (and probably the chem transfer).
One has to consider why treated is used.
Three things: INSECTS, MOLD, and ROT.
INSECTS aren't a big worry in our application - the bees police the area.
MOLD - Many good paints have an anti-mildew addative - paint and keep painted and now worries.
ROT - Elevate your hives and keep them in good air circulation and sunlight and most this problem will be prevented.
So if you look at it from this stand point, there really isn't a significant NEED to use treated.
I'd still say it would be a good CHOICE for hive legs if you use them (as they do make ground contact).