Yes, you'd have to take the engine apart to remove the belt. Like most residential grade small engines, the Hondas are designed (and priced) as disposable units, not really meant to be serviced. That said, I just combined a GCV and a GC into a hybrid (a different thread on that), and they're completely serviceable if you do the work yourself and don't pay labor. You'd never pay a shop for work like this because the labor is far more than the price of a new engine. Just like a Briggs or Kohler engine -- you'd never actually pay a shop to open it up to replace a broken camshaft drive or governor or something -- you'd just re-power the equipment with a replacement engine.
A few pictures of the inside of one of these...captions following each picture.
This is the main cylinder crank case on a GC/GCV engine. Smartly, this piece is the exact same part number for horizontal shaft (GC) and vertical shaft (GCV). The only part that differs is what they call the case cover, which mates to this along that angled flange. This cylinder crank case came from a GCV160 I had that I bought new in 2003 that came on a Craftsman mower. I kept the engine around just in case I needed it. That day came recently (other project), but I share these photos for the timing belt part. In this picture above, the case is "upside down", and that horizontal pocket you see above the cylinder in this picture would be below the cylinder as installed. That's the pocket through which the timing belt passes.
Out of sequence for this thread, but this is the timing belt installed in the GCV cylinder case, with the GC case cover sitting next to it, ready for assembly. You can see how the belt runs directly from the crankshaft up to the camshaft. There are no tensioners or guide pulleys or anything in here. It's just a simple two-sprocket system.
This is the "bottom" cover of the case for the GCV engine, and is oriented as it would be installed on a mower. So this is the "bottom half" to the cylinder case shown in the above picture on the left, if used in a GCV configuration on a mower. I have the crankshaft in it and the timing belt is strung around its sprocket on the crankshaft, just for the photograph. (When you assemble one of these, you do it like in the photo above, and fit everything to the cylinder case, and just move the case cover, whether it's a GCV one or a GC one, into place over the PTO snout of the crankshaft.)
The belt doesn't actually sit in oil, but as the crankshaft spins, the larger toothed sprocket just above the timing belt drives the governor sprocket, which does sit in oil, and the whole works becomes wet with oil pretty quickly.
Another angle, showing the crankshaft and governor sprocket.
Yet another angle. These engines are SO simple. You can pretty much count the moving parts in the crankcase on one hand. Governor, crankshaft, connecting rod, timing belt. That's it. The timing belt transfers the entire valvetrain to the top of the cylinder. So, if you do have a bad camshaft or bad decompression device, it can be replaced from the front or top without opening the rest of the engine, which is not possible with a conventional OHV engine.
This is the exact belt that came on the GCV160 I bought new in 2003. It's 13 years old and mowed a lot grass in southern North Carolina over its lifetime. As you can see in this picture, and in the one below, it looks brand new still.
In my GC/GCV project, I used the GC's timing belt because I knew it had fewer hours on it. But this well-used GCV160 belt looks like it has another lifetime's worth of service in it.
After taking apart completely a GC160 and a GCV160, these engines aren't nearly as scary as some make them out to be. The GC160 died (after 14 years) due to what I believe to be a manufacturing error in the rocker arm area (again, more on that in another thread), but the castings and parts quality in these are quite noteworthy for being "disposable engines".