Not unless you divorce or try to claim EI benefits.
A spouse is still covered as an employee under provincial legislation in most jurisdictions, so technically is entitled to notice, pay in lieu of notice, vacation pay and/or other benefits under Employment Standards Acts. Generally, with a spouse one ignores these items. (Unless “divorce”, as above, in which case the spouse is entirely properly treated as a regualr employee.)
EI: a question of fact. If EI premiums have been paid AND b/c the spouse’s work is equivalent to that of a normal employee and conditions are similar. See: https://www.canada.ca/en/employment-social-development/programs/ei/ei-list/reports/relative.html