I suspect it would be fine. The screws will take the load easy enough, if you loaded a single screw purely in shear with the weight of your drill an 8 or a 10 are not going to fail. Obviously use several screws and it's less risk and you'll avoid loading the screws in ways that'll caused them to pull out. The MDF will be in compression, where it will be strong enough, in pure compression it's pretty strong and you'll be spreading the load over as many screws as you can get in, so the load per unit area will be much lower.
The risk though is the carcass joints, if they get knocked out of square at all the large weight may cause them to fail relatively quickly. Unlikely to be a problem, but that's the most likely mechanism of failure I'd think.
Actually, there's also a risk that the legs will fail, assuming they're on standard kitchen cabinet legs. I'd replace those with something else if you're using them.
I'm assuming they have an 18mm MDF back that's properly glued into the cabinet mind you.
As a belt and braces kinda guy I would fix the 3 x 2 to the inner and outer leaf of each carcass, so that it's also massively stiffening the carcasses. Repeat at the bottom, if you have space at the back to run a 3 x 2 full width there as that'll help hugely. I would use bolts with 1" washers to reduce point loading of the MDF rather than screws. Depending on how exactly you do it, it's worth bearing in mind that MDF will take a tap very nicely and once you've screwed a bolt in it's never going to pull out.
