Fear is a powerful weapon (so, they might joke), other than that it depends on how anonymous you are.
Figuring out where the end point is (the IP they see), is trivial; that can be done with a tracert to it. Then the following logical step is to contact the ISP of the hops and request assistance, gathering its logs and/or connections. Not all ISPs do it, it kind of depends on the laws of the countries the hops belong to.
If they keep repeating it, they could find every hop from the end point to eventually you; only if it is clear that the connections leading to you are the ones they are after. This is where encryption and other nasty techniques which I will not enumerate upon here come into play, in essence they make it confusing to see from which connection certain packets came. Whole such networks do exist.
There are of course other techniques which either involve you (in)directly sharing stuff between the anonymous world and the real world, if a link can be made between both it takes away your anonymity.
So, if you are using the most basic approach (a proxy), it kind of depends how they route your packets further. If they do it straight (which is often the case to obtain higher speeds) and you use it illegally, you can be pretty sure that you are not as anonymous as the proxy claimed you to be. Even if you are really secure, you should still even consider not to play a joke on the government; that's simply unacceptable and even if they can't catch you, they will try to get as far as possible...