Two words: fluidic space. If Voyager managed just fine, the Enterprise can too.
That'd depend a lot on fluid pressure and viscosity and whatnot, tho.
The "operations" in the teaser might be limited to being just below the surface to hide from visual spotting. Or we might see some Jacques Cousteau action to round out the skydives of the first movie and the lava dancing evident here. Won't do to neglect any of the elements.