Yes and no. The UTA has a pretty iron hold on things in the grand scheme of things, being in control of the Warpway and warpship production and licencing. That said, no giant government is without corruption, and some laws are pretty tough for them to enforce - besides this, dictating day-to-day laws themselves is usually left up to individual planetary or system governors.
Accordingly, it's common for some degree of organized crime to exist in most places, as well as some planets, or sometimes whole systems, being more or less the personal domain of a governor who could be equated with a crimelord. Laws that are mandated by the UTA, and not a governor, are usually taken very seriously (no uncontrolled warp tech, no unlicensed teleportation tech, no unnatural genetic modification, as some examples) and are generally only broken by the foolish, powerful, or insane, since the UTA will quickly take direct control wherever issues with those things pop up and generally follow a very simple "kill everything" penal code. This has prevented any long-lived inter-system, serious crime syndicates from being around.
Most people under a Warrant of Liberty aren't subject to system or planet specific laws (or at least can't have them enforced upon them as they can just run the fuck away when need be), so there's many a Free Captain who is more than just a little criminal, strictly speaking. There is a pretty massive grey area there, and being the good guy isn't always the smart choice.
With all that in mind, I don't have any particularly important cartels built, so you have pretty much free reign there if you want it.
Other thing to mention is that for now, you guys are all going to start on the same ship. This can certainly change - warpships generally can't be bought and are financially out of reach of anyone except VERY powerful governors/corporations, but could be taken, earned, or stolen. There will be some teamwork required here.