Yes. A foreign company can have a non-Dutch business address, and thus be registered in the Chamber of Commerce. Then it is still a foreign company, but with a so-called fictitious permanent establishment.
A temporary employment agency from Bulgaria is added in Bouwpas. The company uploads a certified Dutch Chamber of Commerce extract into the system. That extract shows an address in Bulgaria at the business address.
In this case, in that same Chamber of Commerce extract, near the Chamber of Commerce registration number, you can see the text 'This company has no branch in the Netherlands'.
This company will be assessed as a foreign company in Bouwpas.
Please note that the WagwEU (Employment Conditions Posted Workers in the European Union Act) also applies in this case.