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I don't want to say "Yes", but project management knowledge/skills are different than field experience. In project management knowledge there are a lot of tools and techniques to plan/measure/correct time, cost, quality, scope, HR, risk, change, communications, stakeholders...etc.
In the majority of project management processes, "Expert judgement" is the main tool to handle issues.. Then yes, field experience is the main thing here. But project management knowledge helps you to integrate all project aspects in the proper way.
Because a successful project management practical & theoretical knowledge is essential, so certificate is essential, but only certificate will not enough for a successful project management.
most likely yes, some times experience is important but at managerial level also academic knowledge needed as for method of management and analytic process , PMI give a procedure to work with and steps to follow in addition some companies ask for the certificates.