The program will not register you with the UK General Medical Council. However, they will assist you with applying for the MCCEE and MCCQE pt 1. Again this program is for Canadians not for Californians and generally should only be taken if your first choice is to come back to Canada not the U.S. Compared to the Caribbean medical schools, this program has the advantage of a much better reputation, hopefully better teaching (I haven't actually been to a class). The cost is around the same. I did check California's Medical Board and it explicitly lists St. Andrews and Edinburgh on the page. Considering California recognizes medical schools from Afghanistan and 100 medical school from India, I'm pretty sure it accepts most medical schools.
I wouldn't necessarily be wary, but I would definitely find out all the facts before entering any program overseas including the Caribbean. I'm not exactly sure why you trust the Carrbbean schools so much. Many Caribbean schools are unhelpful for finding placements and are for profit. I would take an Irish/UK school over the Caribbean any day. I see advertisements for Caribbean schools everywhere: on the subways, online on the streets and personally, I am wary of any school that needs to advertise itself to attract students.