Short answer. Yes. Article 171 requires each employer and his employees to register with the System, in accordance with its own regulations. Registration is not optional or left to the employer's discretion; the Labor Code states it as a mandatory obligation covering both the employer and the employees.
What the law says
Each employer and his employees shall register with the System in accordance with its regulations.
Labor Code, Article 171 — Registration With The System. Read the full provision →
Registration is mandatory, not optional
Article 171 is short, but its wording leaves nothing to choice: each employer and his employees shall register with the System in accordance with its regulations. The word "shall" makes this a duty rather than a suggestion. An employer does not get to decide whether registering is worthwhile or convenient; the obligation exists simply by virtue of being an employer covered by this part of the Labor Code, and it applies equally to the employees, who are also expected to be registered.
The obligation runs to both sides of the employment relationship
Notice that the article names both parties: the employer and the employees. This is not solely an administrative burden placed on the business; it reflects that both the employer and the workers have a stake in registration, since it is what connects a worker to coverage under the compensation system in the event of a work-related injury, sickness, disability, or death. An employer who registers itself but neglects to register its employees, or the reverse, has not fully satisfied what this article requires.
The details are filled in by the System's own regulations
Article 171 does not itself spell out the paperwork, deadlines, or procedure for registration. It defers that to the System's own regulations: registration happens "in accordance with its regulations." This means the specific mechanics of how and when registration must occur are governed by rules the System issues, rather than by the bare text of this article. An employer trying to comply needs to look to those regulations directly, rather than assuming the general duty stated here covers every procedural detail.
What this means for an employer's compliance
If you are an employer covered by this part of the Labor Code, treating registration as optional is not consistent with what Article 171 requires. The obligation to register, for both yourself as employer and for your employees, exists independently of whether you have ever had occasion to use the system for a claim, and it does not wait until an injury actually happens before it applies. Confirming that registration has actually been completed, rather than assuming it happened automatically when the business started operating or when a new employee was hired, is a basic compliance step this article makes clear is not discretionary.