Of course you can. Though even with tucking, it's hard to fully hide everything sometimes, and it'll tend to move when you swim so I'd kind of suggest a swimming skirt, or boy-swimsuit-type shorts on top for safety - don't worry, many girls wear them.
As for the rest of your body, it all depends on how well you pass. Even though it's probably safe, I'd advise against something like the picture you posted (not just because the swimsuit doesn't fit my tastes). It's quite original/daring and will attract the eye, so if there are some no-pass or hardly-pass points on your body like big waist and small hips, it MIGHT get you clocked. I'd personally go for a more covering one-piece or a "normal" bikini.
But as soon as you pass well enough, restrictions apart from tucking problems are off, since risks are probably very low. Anyhow, if you do any kind of "intense"-ish moving, just normal tucking will most probably not hold, so you'd probably have to use alternate techniques, like taping with water-safe adhesive, or layers (like super-tight holding thing/gaff/whatever, then swimsuit, then something looser for safety).
Hope it helped.
