Considering the way the question is labelled, I would answer that it's possible, but not mandatory for a project to be successful.
A PM may be a resource if the project is small enough so that PM is not a full time job (eg : be their own BA, own dev, own tester, etc...).
I would recommend a junior PM not to be a resource in the team, to avoid the firefighter bias of "I didn't update my risk charter or computed my budget because I was busy fixing an issue in the project".
There are also pros and cons of managing a project comprised of people doing a job we've already done ourselves as resource :
- you "know" what is going on, that gives the PM a better sense of risk appreciation
- PM gets far greater insights in term of estimates
- PM is less dependent on resources to take decisions
- it's awfully difficult not to micro manage : delegation is about setting goals, not the way to achieve them. And having achieved them before, it's hard not to have a strong opinion on HOW to reach them
- firefighting : when an issue arise, it's harder to stay away from it and let the project team do its job
- when managing junior resources, or part time resources with limited availability, they may get the sense that it's OK if they don't deliver as the PM is knowledgeable enough to step up and do it
Now I sense in the question that there is some challenge about the legitimacy of the person claiming PM role to do so, and for this, the answer is quite easy :
- if there is no management involved in this, then it should be a consensus among your team
- if there are external people involved, there should be some sort of governance defining who appoints the PM : it can be your manager, rules such as "the person deadling with the customer is the PM", etc...