The simple answer is yes. If you have an impaired driving conviction on your driving record, that won’t prevent you from getting your M1, M2 or M license. However, note that if your drivers license is suspended, you won’t be eligible to get your motorcycle license until that suspension ends.
Also, if you have a DUI (Impaired Driving) conviction within the past 3 years, no regular motorcycle insurer will insure you, you’ll be forced to get insurance from Facility Association, the insurer of last resort, and your premium will be sky high.