The first question you need to ask yourself is....where do you plan on doing this paid hobby ? If it's Toronto and in cold water, you want to do your DM in cold water and develop a relationship with local industry. Every local dive shop I talked to, before I headed south to do my DM ( 14 years ago ) told me they take a rather dim view of tropically trained dive professionals.
As for pulling into a tropical destination, whipping out the card and asking for work ? I've never seen that happen.
On Utila what typically happens is a DM graduates and then waits in line for a position to open up, usually with the shop that they did their course at and, to be frank, there's a heck of a lot of DMs and instructors looking for work at any given time with preference given to instructors willing to work as DMs
It's really more of a lifestyle position.
On Utila, no problem starting any time you want. Technically you're a customer and the shops want the business.
Sorry if I'm starting to sound like a downer here but the big factor is really how much time you have to do your course. If you're planning on doing the course in as little as three weeks then you might be better off simply going diving and picking the DM/Instructors brains on the boat. If you have something like 6-8 weeks then taking the course may be the better way to go, bang for buck wise.