My 04 6.0L sits for about 4 to 5 weeks at a time. Then I start it up. And then I drive it. Then I park it. Then it sits again. The only problem I have had doing this is the dust on the windshield gets pretty thick. My original batteries lasted 122K miles.
The VGT turbo does build up some soot, as many have commented on. Mine is throwing a code right now (P0299 - low boost). So, I will take it off, clean it, and put it back on. With 135K on it, it is probably about time. Diesel is a dirty business, and the soot will build up some. But not from idling for a few minutes. And putting your foot in it will not blow out the soot. If that was the case, mine would be clean as a whistle. But a couple hundred tanks of fuel run through it, and some soot will build up. Look at the end of your tail pipe. It was not black when you bought it.
And if you do put your foot in it, and see a cloud of black smoke, that is not soot. It is unburnt fuel. Your injectors will send more fuel into the chambers than they can burn. So, out the pipe it will come. Some people think this is cool. I don't really like it coming out of my truck. But I do like seeing it when I start my tractor.
So, don't worry about it. 2 months sitting is really nothing. However, if you are worried about the batteries, disconnect them. The electronics will draw a very small charge (.1 volt or so) even when the truck is turned off.
And, I hope you recover from surgery real fast. I have heard some pretty bad stories about ruptured appendix's. I am glad to hear yours was not one of them. :thumbsup: