It all depends on what type of plastic they are but you've got the key - tieing them down securely makes all the difference. If you can run ratchet straps over them and still have them easily accessible then it's worth a shot.
The easy access thing is the hard bit, though, I tend to find that at least half of my gear needs to be 'easily accessible' and stacked containers don't lend themselves to that sort of convenience.
Certainly a lot easier that building a drawer system though, and if you've already got them just go for it - do a weekender and see how it pans out for you.