The boards do stay flat and joined together if you do the soldering well. You can always put eg. a thick piece of thick cardboard underneath to protect the bottom of the PCBs.
So durability / basic functionality wise, there’s nothing stopping you from using the build without a case in a tidy home desk environment for a while.
The obvious issue / nuisance is, that as long as you don’t have any kind of front panel, all the 4x4 silicone button grids on top will be loose - even though they slot into the key holes in the PCBs. They’re going to be much less precise and fun to use without a proper “shim” or a thick front panel, as they are quite high and wobble around a bit when pressed (and bleed light to adjacent buttons somewhat). Plus when you forget they aren’t really attached and move the unit around, they drop off and have to you’ll curse a bit and put them back again. (Happened to me a couple of times when I was thinking of something else)
So while it’s not ideal, it’ll definitely work and you can use the DIY grid until you can get the funds together for a case of some sort.
(Edit: with the disclaimer that I’m not very OCD at all, if you find yourself often getting frustrated about details and things being a bit clunky and working in much less than ideal way, then it could be a problem…)