A degree may be important, but not important enough to matter
"Will it guarantee you career progression in the profession?" No. But it will give you an edge against candidates for a position that don't have as many credentials, all other things being equal in the hiring process.
"Is it important?" Sometimes. But the unasked question "Is it more important than...?" is the equation one needs to construct in order to have a meaningful decision arise.
To start with, it really depends on the degree and area of specialization. We almost don't want people with "hr degrees" for business partners, but we love them for central hr orgs, centers of expertise, and shared services -- especially the PHR* stuff for generalists (not so much business partners), when experience is light. When experience is substantial and shows continued education and awareness about best practices -- or, even better, when the person is question was on the cutting edge of establishing best practices, or perfecting them -- that's what really makes a difference.
For a person without experience, coming from a degree program, we want to ascertain whether you have learned some useful tools and skills in the degree process, ideally through application of academic learning via internships, etc.
So, to return to the question at hand, the question to ask is: Would entering an HR degree program and taking on student loan debt etc get you further in the short term and further in the long term than spending your time and money on other things (an MBA? or just getting an HR job in an org that actively grows their people?). I think "that depends," and varies from individual situation to individual situation.
So, Yes, it's important, but maybe not important enough to matter.
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UPDATE: The CLC just released a study which might answer this question (at least in the context of the mostly US companies they investigated. HRBP effectiveness:
Education/Certifications -- least effective
Motivation (to be in HR) -- twice as effective as Education/Certification
Experience -- twice as effective as Motivation
Competence -- more than three times as important as Experience
(The full study is available to members. It's called: Building the Next Generation of HR Line Partnerships.)
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* And/or:
PHR-CA - Professional in Human Resources California Specific
SPHR-CA - Senior Professional in Human Resources California Specific
U.K. CIPD - Level 3-7
Certified Professional (Australia HR Institute)
HRA - Human Resource Associate (Singapore SHRI)
HRP - Human Resource Professional (Singapore SHRI)
SHRP - Senior Human Resource Professional (Singapore SHRI)
GMS - Global Mobility Specialist (Hong Kong IHRM)
GRP - Global Remuneration Professional (Hong Kong IHRM)
CHRP - Certified HR Professional (Canada CCHRA)
CEBS - Certified Employee Benefit Specialist
CCP - Certified Compensation Professional
CBP - Certified Benefits Professional
CPP - Certified Payroll Professional
CHRP - Certified Human Resources Professional
CMS - Compensation Management Specialist
FPC - Fundamental Payroll Certification
GPHR - Global Professional in Human Resources
GRP - Global Remuneration Professional
GBA - Group Benefits Associate
RPA - Retirement Plans Associate
SPHR - Senior Professional in Human Resources
in addition to PHR - Professional in Human Resources