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missed your reply. it's 18mm. the screws that come with the fasteners i mention above are 14.4 incl the head i think and the thickness of the fastener is 2mm so should sink about 10mm in which is probably fine if i use a decent amount of them spaced out.
What thickness of ply? Can you screw from underneath the frame using screws just shorter than the combined thickness of frame and ply? Once you have stuff on the desk, plus the weight of the ply, you won't need much penetration to hold it in place.