There is a big difference between heavy truck non-synchronized transmissions and a synchronized in our dodges.
With a non-synchro trans, there is nothing to get the mating gears to the same speed. So - you have to match the engine speed to the rpm needed for that gear. If you have the clutch pushed in, the engine does not turn the input shaft so you cannot control the speed of the gears. Hence - you need to have the clutch released in order to "manually synchronize" with the throttle. Many drivers use the "double clutch" method ... clutch in to get out of gear easily, then release clutch and match engine speed, then stab the clutch again to ease make sure there is no load on the gears as they are engaged. The nice thing about a non-synchro trans is that you can feel the gear cogs and more easily tell what engine speed you need.
For our transmissions - shifting without the clutch is tricky and you need to use caution. If you match the engine speed perfectly - there isn't any issue and the next gear should fall in. If you don't it is hard to tell because you are up against the synchro and cant feel any grinding. At this point if you just pull harder, you are now making the synchronizer try to match the engine speed to the vehicle speed. It is not designed to do that - and that is where damage (or accelerated wear) can occur. The synchronizers are designed to speed the input shaft and clutch disk up and down, not the whole engine. Double clutching is probably the best approach as this way you get the gears to almost the same speed, and then the synchros only have to do a little work.
Whew - too much writing but hopefully it makes sense!
Mathew