Need an alternate way to install hand-spray bidet on my toilet - can I Tee off the 3/8th input valve?
You should be able to do what you propose because the adapter/valve that came with the unit does not appear to have any sort of pressure regulator built into it, meaning it appears to be designed for normal household pressure (btw this is not the case with all hand-held sprayer units).

Because the consequences of failure could be catastrophic (e.g. flooded house) I would hook it up but closely monitor it for a while to confirm no leakage, hose swelling, etc.

Oh, and turn it off when you go on vacation...