Yes. Happiness is part of the character-management layer and community testing links low happiness with reduced ability to manage staff expectations and continue normal routines. [topic-1]

What to do

  • Do not let sleep, food, health, and happiness remain neglected while scaling the company.
  • Use activities available to your character and check the happiness response.
  • Resolve character needs before diagnosing an employee-management problem as a store bug.

Why this answer holds

The official game description explicitly requires the character to sleep, stay healthy, and stay happy while building the company. [steam]

Version 1.0 check

The collected sources do not establish one fixed numerical business multiplier for happiness, so this page does not invent one.