Anyone is eligible to take the exam, but if you pass you may not have enough relevant experience to qualify as a CISSP in which case you would need to opt for Associate status.
The experience requirements are set out here: https://www.isc2.org/Certifications/CISSP/experience-requirements
My recommendation is to review the exam outline: https://www.isc2.org/-/media/ISC2/Certifications/Exam-Outlines/CISSP-Exam-Outline-2018-v718.ashx
Take a look at the tasks/subtasks associated with each domain and figure out if you have 5 years of cumulative experience covering at least one task/subtask in at least two of the eight domains.
NB - physical security is no longer its own domain, but of course it is still a fundamental aspect of the CISSP curriculum. Rather than being its own domain, it now features across at least two domains as stated in the current CISSP exam outline:
Domain 5: Identity and Access Management (IAM)
5.1 Control physical and logical access to assets
Domain 7: Security Operations
7.15 Implement and manage physical security
» Perimeter security controls
» Internal security controls
So you may already be covered for the experience requirement.
As to your questions about it helping you with your career, it certainly won't hurt!