You absolutely do not need 10 years to be able to apply to enter Canada. 10 years is required for what they call Criminal Rehabilitation. A CR essentially erases your DUI to Canada so that you can travel there anytime you want without restriction. If you do not meet the 10 years you will have to get a Temporary Resident Permit. It is a basic application and, with a Job Offer from a company that operates into Canada, is almost a guarantee to get one. I guarantee you there are vast amounts of pilots in the industry that have DUI's. DUI's are much more common than people think and I know pilots with them that frequently travel into Canada.

Having said that, any regional will require you to be able to travel to every country they operate in. They may interview you and give you a CJO before you prove you can enter Canada, but they will not allow you to start class without showing them a travel permit to Canada (TRP or CR).