Undermounting a non undermount tub

So, I'm wondering if I can undermount a drop in bathtub that has not been specifically stated as "undermount" capable? It would seem that for cast iron tubs, the sidewalls would be more than strong enough to just sit there under the deck and then I could caulk the deck to the top of the tub.
In the acrylic/fiberglass tub variety, it seems like I could install it as a drop in in a typical deck configuration (i.e. in a typical deck frame) and then build an actual 2nd top (show) deck over the top of the tub (and sub-deck).
Any thoughts?

tub

NONE of the tubs should be supported by their rims, so you install the tub with whatever support it needs under its bottom and then construct the frame around it, either above or below the rim.