You'll get time alignment issues, especially if it's a 3-way or basically more than three drivers. First off, if you're too close, tendency is that you can localize each driver more. Second, even if you have a 2-way, 2-driver floorstander, the question is whether you can mount them properly relative to your ears. These were voiced with a mic at LazyBoy levels at around 1.5m away from the center point between them; the typical office chair and computer desk are higher than that and you'd be sitting closer. So basically using a floorstander won't really mean it's as easy as putting on each side if you're after sound quality.
It's relatively easier to use 2-way speakers nearfield, even if they weren't designed/tuned/measured for such use because you only have two drivers, because not only do you have only two drivers on each side that will need to get sound to your ears at the same time, but also because in a standmount/desktop form factor it's relatively easy to mount them so the tweeter or midrange or midpoint between them is at your ear height. Even professional monitors that have more than two drivers, like some 3- or 4-way JBLs, aren't floorstanders, but horizontal stand/deskmount speakers, so time alignment for height won't be an issue. In fact they cluster the drivers together as close as possible to get around any kind of time alignment problem for all those drivers.
Ideally, I'd get a new desk to accommodate standmount monitors, given you'd need more than 7IN on each side - the typical 5IN monitor is already at 7IN minimum (driver diameter 5in, wood panel on each side usually 0.5in to 0.75in plus a bit of space inside), and with two 24in displays chances at nearfield you'd probably need some toe-in to make the soundstage more precise. If you really can't replace the desk, get the floorstanders, but make sure you stick to 2-way speakers, make sure the port isn't too low on the speaker or it might pull the bass downward, and try to get them at the proper height relative to your ears in case they're too short.
