As the man says, they can be effective, often, but not always.
They are just one of many factors contributing to any outcome.
I have used them a lot, my most common one being, "May I attain to full awakening as quickly as wisely possible for the benefit of all beings," which, while being a bit convoluted, nevertheless did help galvanize things.
I also made resolutions to attain to paths, to jhanas, to Nirodha, to powers, to many other things, and I think they help program the mind at some core level to actually accomplish what it can accomplish.
However, they can't force the process beyond what it can to, so this is an organic thing that will only go so far so fast. I have cooked myself a few times by using resolutions to push myself deep into territory I couldn't handle in my more gung-ho days, and that often caused difficulties, though I made relatively fast progress.
The most interesting thing about resolutions, aside from being powerful, is that they tell you a lot about what is going on right now, where you are at this point, what you are reacting to, what drives you, what forces are in play now, and that tells you about suffering, as that is what drives that, so look at what is driving you to resolve and see that directly at the sensate level: that's powerful practice.
Also, notice that resolving is a stage dependent process: some stages are much more likely to cause us to want to be somewhere other than we are, such as the Dark Night. Thus, balance effort and acceptance: easier said than done. See that goals occur now, effort occurs on its own now. These are key insights to see again and again. The more of the sensations that are present now that you are able to see making up your future achievement trip, the better you will do.