Regardless of the tire clearance, could I use my carbon road bike off road too? Can it handle the stress and load? Wont it break ? Does a road bike needs to be more robust to handle the offroad, gravel load?
The strength of a carbon fiber composite frame is not the problem. There are many CFC gravel, cyclocross and mountain bikes, so obviously CFC as a material can take the impacts. If you ride a road bike on a harsh, bumpy paved surfaces it does not break. If you want to be convinced of how tough CFC frames are, google for videos of the testing that manufactures put them through.
The primary features that make a gravel bike more suitable for bumpy and loose surfaces are stronger wheels, larger tires run at lower pressure, slacker steering geometry and longer chain-stays.
There are several answers to this question. The one is fair use. Like you wouldn't ride a roadbike on a severe downhill or in a cyclocross race. Or have a 150kg rider on a lightweight racebike with flimsy, sparsely spoked wheels.
The other answer is given by the limitations imposed by the manufacturer of the bike and the components, mainly the wheels but also for some other essential parts like handlebars, stems and seatposts. There are quite often limitations for rider weight and use of the bike. Many of these are given by the limitations of the material but some are for reasons of legal liability and warranty. The Trek owner's manual is a good example. Link: http://bike-manual.com/brands/trek/om/welcome/index.htm You'd look under use conditions.
Still some things can't be avoided, like having an overlooked pothole, a harshly cobbled stretch of road or short bit over not yet properly resurfaced road repairs. You may have to adapt your riding style, speed and behaviour to the conditions.
One last thing, a carbon frame or carbon rims don't exclude from using the bike on forest trails or other difficult terrain. There are full carbon cyclocross bikes and mountain bikes. On the harshest road race, the Paris-Roubaix and on the Belgian one day races in Flanders that cover long stretches of awful cobbles about all riders will go on carbon bikes.
See this video for a particularly nasty stress test of a carbon frame. Specifically note that they replaced the shock with a simple metal tube. It simulates a hard hit without any suspension (not even tires).
Generally, carbon seems to be pretty strong. The reasons that it still has (had?) a reputation to be more troublesome are these:
So the question is not whether carbon road bikes are good for offroad use, but whether road bikes are good for offroad use. And this depends solely on your riding technique. Your body weight is several times the amount of bike weight, and can be an incredibly effective spring; what you do with it matters a lot more than the material of the frame.
While it's far from ideal for the task, I've done quite a lot of gravel riding on a road bike. At the time, I was riding a rim-brake Scott Foil (2017 model) with carbon wheels. I never found that the frame or componentry was at any risk of failing on me at any point. You will probably get a number of small stone chips in the paint job, but that is just cosmetic rather than a structural concern.
The main issue that I had was the braking performance on loose surfaces was just awful. I was running carbon rims, with 24mm tyres, so I needed to start braking long before any turns. On one ride, I had a flat tyre while riding down a very steep gravel descent and was unable to come to a stop for several hundred meters because my rear tyre had even less traction once it went flat. The issue of traction on narrow tyres is a major consideration that you will need to learn to handle through every corner.
Speaking of handling, your road bike is likely to have narrower handlebars than an equivalent cyclocross or gravel bike, which will affect how well you can manoeuvre your bike on very rough terrain. You can swap out the handlebars for something wider and the stem for a shorter one, but road bikes are built to handle well at higher speeds and their geometry is designed around that.