Seashell, the clear answer to that is: "possibly".
See:
http://www.state.gov/documents/organization/86576.pdfesp article 7c
The FBI's role seems officially to be more liason and coordination than investigation when abroad (and it helps if there are hostages, terrorism or transportation issues). You can see how it would be awkward for the locals if they tried to conduct a formal investigation on foreign turf. But by their charter they do get involved in drugs, sex with minors and organized crime, so if they think any of those are important elements here, they may elect to get into their "liason" and "coordination" roles.
http://en.wikipedia.org/wiki/Federal_Bureau_of_InvestigationBut then, it's the FBI and as we know, they pretty much do what they want (like the CIA, DEA etc) regardless. They get to decide what they do, not some silly laws or rules laid down by some silly congress or silly constitution.
Interesting (and predictable) how the US embassy in Guat told JM to basically get lost. A lot of Americans think their embassy's job is to help them no matter what, but that's basically a myth imho. The truth is closer to: they will almost never do anything for you if you run afoul of the local constabulary, unless it's an expired visa issue or something mundane like that, and even that is only sometimes. With accusations of drug involvement, sex with minors, gang associations, murder etc and I suspect, obstruction of justice, they pretty much assume you are guilty till proven innocent and will give you the major brushoff. Why should they risk frosty relations with host country on behalf of ol' scumbag you? Or that's what I hear, not having any direct experience in these areas.