Hard to do the experiment, as you need two countries with otherwise identical production practices, where one washes and the other doesn't. For instance, the US and the UK would be a bad example, because egg producers in the UK generally vaccinate for salmonella, while those in the US don't; regulations on things like cage sizes also differ substantially.

You also need identical reporting regimes, which may actually be a greater problem; salmonella is not generally a mandatory reporting thing, and many people infected with it don't go to the doctor with it anyway; if you're a healthy adult it's pretty much just nasty food poisoning.