I always think of formal qualifications as working on one dimension only. It's a comfort factor for employers because it reduces the unknown about applicants by one important element, but they can't legislate against non-fit in other factors. That means there's still a lot of latitude in the recruitment process, because people don't just hire qualifications, they hire people. Pick the wrong character, and you'll end up with disruption and a deeply unhappy team.
Whether you get considered on experience alone depends on the attitude to risk of the employer. Some will, some won't. You'll probably get more rejections, but it's only because of the level of risk the prospective employers are willing to take. At the end of the day, I believe a lot of companies would rather do without the qualification if they are persuaded that the person is right.
Your best bet is to make the front end of your CV really strong. Be very aware of the nature of the organisation you're applying to, and make this section 'fit' as far as you can with what you know of their corporate personality. Go on their website and see what terms they use to explain what's important to them as a company. Throughout your CV, tell them your story using their words and terminology.
Make sure you have an attention-grabbing career objective up-front that makes the employer think: 'I want this person because of their...' ambition, experience, ideas, spirit, organisation skills or whatever. If you catch their eye here, you have a good chance of them reading on, and if the rest of the story is good, you have a chance of them thinking that they want you as a person, and will be willing to overlook the formal stuff.
Next section needs to highlight your key skills - what you'd bring to the table, so the reader is in no doubt of the level of your experience.
In your case, I'd be inclined to add a section on 'career highlights' - one sentence on each of five or six key achievements, including any numeric values, such as budget, revenue, profit, numbers of people, measures of time etc - so that you can show that you've done many of the things they'd usually expect from someone formally qualified, and at a similar order of magnitude.
In order to know how to best handle your qualifications and training, I'd have to know what they are, but if your qualifications aren't so impressive, I'd tend to lead on relevant training, and put the quals underneath. A trick of the eye is to 'hide' this section, so it's about 3/4 of the way down the page, as the eye tends to focus at the top and bottom of the page and skim this bit.
Hope this helps.