I asked about this just to be sure and no, a desk might be found in the "escritório" department or store but all things "office" go under "escritório" and this includes staplers, paper clips, filing cabinets, and [desk] computers.
A desk is a carteira, secretária, mesa (even, "mesa de escritório"), balção, recepção, or, serviço (depending on which kind is meant like classic desk, student desk, computer desk, help desk, reception desk, etc.). If anyone uses "escritório" to mean "desk" in Portugal it is likely close to the border with Spain (not so much the Galician part) but, I imagine there is some Portunhol mixing like this on the interior edges of Brazil as well.
Funnily enough, there is an "Escritório Portugal" kit for a very particular (unvarying) desk set-up but those are all Brazilian companies.
Otherwise it is Mobiliário de Escritório or Secretárias de Escritório.
Well, here is a great site to explore for "escritório" vocabulary:
To Anglophones, there are two kinds of offices; a work-based office (obviously referred to as an office) and a home-based office (usually, but not exclusively, referred to as a study). Is there a similar distinction in Portuguese, or do you refer to them both as escrotórios?