I've done a kind of tye-dye with my diapers but not exactly. I was never brave enough to do an actual tye-dye with elastics and everything. I just couldn't figure out how to tie them exactly and where exactly I'd put them dye etc...
So I just kind of winged it and later found out that the technique actually has a name! Who knew! It's called drip-dying. You mix up the tye-dye dye solution, soak your diapers in soda ash, all the same as with regular tye-dye. Then I just lay the diaper flat (I put plastic wrap underneath to protect the surface and then use this to seal up the diaper while it cures). I put the dye in these little plastic syringes (no needle or anything, just a little plastic tube at the end that I snipped off, these are what they gave us at the hospital to finger feed a breastfed newborn) and just gently 'squeeze' it out where I want it. I get pretty good control though there will be spreading of the color so you have to be careful not to put too much so that one color doesn't 'invade' the whole fabric and also make sure that whatever colors you use next to one another look good when mixed. For example, yellow and blue go well because they form a green when mixed. Red and green aren't good because they just form a yucky dark brown/black. That kind of thing.
I've made all kinds of random patterns or done half/half diapers. Or my favorite is to 'progress' from yellow to orange to red in one diaper, that's a cool effect... I've done stripes and also solids with 'speckles' of another color on top, all kinds of stuff. The effect isn't exactly tye-dye because the colors don't usually blend in as much, but then you have a lot more control and can get way different effects.
If you do end up doing some traditional tye-dye I'd love to see some pics and would love it if you told me exactly how you did it! Good luck!