An offshore account in USD - yes they can. At an International Bank located in Belize - no problem.
Local accounts - probably not. Central Bank is being super tough in their approval process for local checking and savings accounts - seems ridiculously harsh to me, but that's how it is unfolding right now.
I'll tag team onto Diane's comment and simply say that I doubt he'd walk in with the requisite documents and walk out with a local bank account. The process has been made more difficult, but not impossible, as a result of the passage of FACTA and the pressure brought to bear on the banks largely by the US. Belize continues to be one of the most staunch in maintaining its stance on bank privacy in the offshore account arenas even when bank giants like the Swiss have caved. As a result though the local banks, like Scotia, Atlantic, and Belize, are being very cagey about opening new personal accounts. You might want to have you friend review the FBAR requiements put in place by FACTA before moving his money around.
We own a vacation condo and went through the process to get a savings/ATM card locally for convenience last October. We tried Scotiabank and they were utterly ridiculous--finally agreed to give us a non-interest bearing account for a monthly fee!! SO we went to Atlantic Bank and walked out with an account that day, interest bearing (4% I think)and no fees. They spent the next couple of months working with us to get the paperwork right but were easy to work with. We did have some paperwork with us and they requested what we didn't have. Check their website for specifics. It certainly is not like opening an account in the US. If you want specifics on what we gave them send me a PM.
We opened al ocal savings account with Atlantic before we lived here but it was a long and painful process. Be prepared to make several in-person visits. They used to have a page on their website that said what you need to open an account as a non-resident but I cant find it now. Maybe they've changed the requirements. We needed to produce everything on the website plus quite a bit more documentation. My husband opened the account just over a year ago and it took until December 2011 to get me on the account with him.
Yes you can open a basic account at Banks like Atlantic Bank, If you dont live here or have a work permit or residency. Every one has a different story. Everyone thinks its a set in steele law. The requirments from the bank is a bit of work but no real problem. They will ak for alot of documentation but in reality it takes about a day of your time to do what you need to do. The offshore banking stuff is for big money, very simple to get a personal account, if you are smart about it. We own land now, but we opened our bank account after our first visit. Its all about attitude and how you come across, My husband got his residency never even spending a year in the country, with no bribes, no paying anyone...its just an individual thing...respect..respect..respect..lots of gringos have a hard time with that.