Just got a set of 30mm cross tyres for my road bike. It's a carbon audax. Will I die if I ride off road on it?
Your brakes will be sh!t and the tyre may not fit through the brakes.
Depends how offroad 🙂
No but you'll probably crush your nuts if you stall and have to get out of the saddle quick...
Which is why we use mountain bikes
...but you already knew that (unless you're 14)
Depends what you mean by off road really.
If you mean towpaths and fire trail type riding, you'll be just fine. An audax bike will have clearance for the larger tyres and more forgiving geometry so comfort shouldn't be too much of an issue. Apart from mud clogging things up (avoid overly muddy routes) only issue might be the carbon frame which isn't necessarily built to take the knocks it might get being ridden off road.
If you mean taking it down Jacob's Ladder or somesuch, you may wish to invest in a dropper post before you set off.. 
I found my Condor Fratello had it's limits.
Running full length guards didn't help much with clearing mud, and I felt too far over the front on steep, slippery downhill sections. Actually, drop-offs weren't much fun either, and I've got good strong wheels too. It's fine on greenlanes in the dry/damp, as long as the lanes aren't too rocky, as I can only get 28's in it, and they don't have the volume to soak stuff up. It does end up getting carried in the mud - not because I'm precious about it, but it clogs up and it's just easier to carry it before it fills up with mud, than drag it along once it has.
😉
None of that is a criticism of course, just horses for courses.
When I first bought my retro steel road bike last year, I set off for a local bumble around and ended up on my usual trails through force of habit and lack of planning. Few drops (nothing rocky) and plenty of rutted, muddy trails. Didn't die, bike still works, still bunny hop all over the place and it still hasn't snapped.
Back in the day, before mountain bikes were invented, we rode our bikes offroad....you do need to fit cowhorns and remove the front brake though... 🙂
Martin Ashton:
(skip to 1 min for the off road)
The tyres fit nicely and I'll just be doing bridle ways etc, maybe a bit of the SDW...it's really for stuff that my ibis is overkill for. Just wanted to check I wouldn't kill the bike really...
You should be okay, as a youth I did the Ridgeway on a 531 framed bike with mudguards. Stuff like that was quite common.
Cross bikes aren't beefed up road bikes, and the original MTBs were just skinny tubed bikes.