Can the word "desk" be used as a verb?

Solution 1:

The expression appears to be from journalistic jargon:

Desk Rejected

... A desk reject means that the program chairs (or editors) reject a paper without consulting the reviewers. This is done for papers that fail to meet the submission requirements, and which hence cannot be accepted. Filtering out desk rejects in advance is common practice for both conferences and journals.

(avandeursen.com)

Solution 2:

As noted, your example is probably not desk used as a verb.

The Oxford English Dictionary does list desk as a verb, but it is marked obsolete. Nevertheless, here is some information about that obsolete verb.

1. transitive. To fit up or furnish with desks.
  That the said Chapell be desked.

2. To place in or as in a desk.
  A leafe of that small Iliade That in a wall-nut shell was desk't.
  Then are you entertaind, and deskt up by Our Ladies Psalter and the Rosary.
  I..saw many curious relicks desked vp in the side of the wall.

3. to desk it: to work at a desk, do clerical work.