Are there any scenarios where you can run a flexible cord through a drop ceiling? I was told we could run a cord from a box above a ceiling, through the tile, with a cord connector on the end. This is for an appliance that is in the middle of an institutional kitchen, away from the wall, so we can't use a fixed receptacle. 400.8(2) seems to not permit this, but it also says, "Unless specifically permitted in 400.7..." which could then refer to 400.7(6)&(8). I questioned this whole thing at work (without citing the actual code, I didn't have it with me at the time) but the foreman said it was OK to do. What do you think?

400.7 says nothing of passing through ceilings. it speaks to cords for equipment.
400.8 is the guide.

I would install a ceiling box and drop a cord with strain relief and twist lock cap.Don't forget,if it is 120 volt 15 or 20A GFCI is needed. 210.8(B)(2)

Passing a cord through the ceiling tile, as you describe, is a code violation in two ways: there's a flexible cord above the grid, and the cord is passing through a partition.

That said ... I recognize that this is often done, and that circumstances often make even a ceiling box impractical. I'm not quite sure where to go with this ... maybe a proposal for the next NEC cycle - but I'm not sure how one would write it.

Drop ceilings, once the 'wunderkind' of building, are quickly becoming a major headache. Perhaps their time has passed.

Another old addage from NJ....

"Drop ceilings hide a multitude of sins"

That said, cord thru the tile is a no-no. A ceiling grid mounted box, suitable coverm strain relief, & TL is accepted

However, a TL recept mounted in the ceiling box, face down, that the cord from the equip plugs into may be a better way.

Some AHJ's cite the cord from the ceiling box in the first scenario as using cord for permanent wiring, and red flag this, absed on 400.7 & 400.8 interpertations.