Yes and no. When you are more junior in your career - yes. What you must understand is that visas are processed by bureaucrats. Our job is to make it as easy as possible for them to say yes. So the CV and the JD and the country’s experience requirements and the references must all line up. Your job is to make it easy for them to say yes. Many countries want 4 years of experience for each equivalent year of a degree course. So if you are early in your career, the degree is very important.
HR (actually TA - Talent Acquisition) are gatekeepers. You need to write a CV for two audiences - TA and the hiring manager. Sometimes (often?) they can be opposites. What I look for as a HM is the way you think. What TA often do us keyword matching. That makes it hard to write a good CV.