Answer
Yes, you can open a company in Uruguay with a foreign passport, and local residential registration is not required. A foreign passport is sufficient to do so; local residential registration is not required for this process.
A passport addresses only part of the task. Depending on the type of business entity, you may need an address for the procedure, tax information, representatives, registration with DGI and BPS, as well as documents for the bank and incorporation formalities.
It is important to distinguish company ownership from a person's right to work. Registering a company does not confer automatic immigration status or substitute for real business activity. Therefore, opening a company with a passport is possible, but launching the business still requires an appropriate business structure, bookkeeping, banking arrangements, and compliance with obligations.