I really want to make the SW coke gammon in the slow cooker, but I'm going to be out of the house for around 6 hours is it safe to leave it unattended?
We've slow cooked gammon in (full sugar) coke before, and what happens is that all the CO2 comes out in the first few minutes as it comes up to temperature. So if you start (as we do and most recipes suggest) by bringing the cooking liquid to the boil the foaming will happen while you're standing over it.
This makes sense as gases are less soluble in hot liquids than cold; in fact I've used heating in the lab to drive off dissolved gas.
Most of the sugar is poured away in the cooking liquid, so there's not much benefit (in terms of calories) from using diet. If you plan to finish the gammon off with direct heat for browning, sugary coke is likely to give a nicer finished item (colour, flavour and smell). Some sweeteners go bitter when cooked too hot (and the reaction products may not be good to eat), while sugar caramelises.
If you're asking in reference to the artificial sweeteners, I'd say it's probably not a great idea, but not necessarily for safety reasons.
Aspartame is the most common artificial sweetener, and the one used in most varieties of Diet Coke (apparently there are some, less common that use Splenda).
There are a lot of claims about health risks of aspartame, however, the general laboratory-tested medical and scientific consensus is that it's relatively safe. When aspartame breaks down, it breaks down into Phenylanaline, aspartic acid, and methanol, mainly, and also formaldehyde. The ratio of the first three are something like 4:5:1. Keep in mind what makes a sweetener "low cal" is the fact that much less of it is needed to attain the sweetening. Overall, as it breaks down, the exposure, though daunting to read or hear what it breaks down into, is really fairly trace and does not cause harm. I suspect people would never eat if they realized all the by-products we are regularly exposed to.
So, this "break down" happens in our natural digestive processes, and we are exposed to the components. When aspartame is heated, it starts breaking down, without our digestive systems getting a chance to work on it. Does this somehow expose us to MORE of those substances? I don't believe it does, it just happens before initial ingestion if it's already breaking down.
However, if the heat is making it break down, that means what is in the heated solution is no longer aspartame, but, rather, phenylanaline (an amino acid), aspartic acid and methanol. That combination probably does not deliver the flavor sweetening because it is no longer, molecularly, aspartame, the sweetener that gets its sweetening characteristic from its molecular structure.
I suspect your taste will be markedly different if any significant amount of the sweetener breaks down (which usually happens after it's traveled past your taste buds and into your digestive tract) into its component parts before you ever get a chance to put it in your mouth. If you slow cook it, that's a long time heating and breaking down the sweetener.