There isn't a single answer to this, there are many failure modes for a transmission. If the torque converter goes then it's pretty catastrophic event, all your transmission fluid will spew out and it will be a smoking heap. More likely in your case a gear will stop working, or the whole thing will just grind on you. It's not likely to give you any audible warning.
It's not a particularly high risk safety issue, for instance a brake failure. It's not going to seize up on the highway, the worst case is you will suddenly have no power to the wheels and you'll coast to a stop, which is unfortunate but not usually that dangerous a situation.
While I understand what your mechanic is saying, it all depends on how long you plan to keep the truck. Although it could be your transmission is on its way out, clunking into gear is a classic symptom of old, broken down transmission fluid, in which case a service could fix it. What your mechanic is saying is that once you open it up it could be a can of worms. The theory is that disturbing the fluid could dislodge gunk that could later block valves and cause a catastrophic failure. There is some truth to this but it can be overblown sometimes. If you're a mechanic it's an easy answer to a thorny issue, but it's not always the right one for your customer.
The problem you have is going to get worse, with more clunking and slipping, and eventually a complete failure. Remember that transmission fluid is not only a hydraulic fluid but also acts as a lubricant, once it breaks down too far it loses its protective properties and your transmission starts to wear badly. If you are only going to have this truck short term you'll probably be fine. If you need to keep this truck longer term you've got to deal with this issue, and you have a few servicing options:
- A transmission fluid flush: when you drop the pan out of a transmission only about half the fluid comes out, the rest is all trapped in the hydraulics. A flush gets all the old fluid out. I would not do this with an old transmission such as yours because this is where the biggest chance of dislodging crud lies
- Fluid change service: a fluid change service drains the available fluid and replaces the fluid filter, it's relatively non-invasive process, but it can in some cases cause issues
- Replace fluid without dropping the pan: this is something you can do yourself. You'd stick a syringe with a long tube on the end down the filler tube where dipstick goes, suck the fluid out of the transmission (do not try to do this while it's running! You also want the fluid to be warm, not hot) and replace it with fresh fluid of the same quantity. This replaces the fluid with fresh without disturbing anything. The benefits of this approach are it's super-cheap, and it won't make anything worse. You may have to repeat the process a few times, running the engine to circulate the fluid, but eventually you'll have mostly fresh fluid in there
I would suggest you try option 3, as it's a low risk and cost effective way to try and fix the problem. It may not solve it but there's no harm in trying.