Treated lumber is safe from mildew and insects when wet. It isn't
from weather, or from moisture fluctuations, you want to STAIN IT for
any kind of aboveground use.
Most good glues for outdoors are rigid and waterproof. Rigid is bad,
because your wood will stretch/shrink in weather. A lot. The glue
crack. Waterproof, oddly, is bad too, because it will block movement
of moisture. On dry days, your glue-wrapped tenon will still be
when the mortise it is in has shrunk, and the size mismatch causes
wood to split. On wet days, the dry tenon will pull free of its glue
as the mortise wood member swells.
I'd recommend a few dots of hot-melt glue. It's flexible, though
weak, and won't wick on the wood to make any effective moisture
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