Is caulk sufficient to seal around my new bathtub?
No, that's not sufficient.

I would epoxy a flange to the tub.  And then for good measure use some roofing tape (which is flexible) to backstop the flange.  And maybe for really good measure install a pan under the tub, or a the very least some building paper leading to a visible spot below (so you quickly detect any leak).

Remember that most building materials can survive getting wet periodically.
No building material can survive staying wet.  Trapped water means mold, rust and worse.