Will the roof cave in?

It won't necessarily cave in, you'll just fall through it if you step in the wrong place. The plywood is about distributing load over the supports in the roof structure, not about making the whole structure stronger.

When my brother dropped through a ceiling because he missed a joist in his walking, straddling a joist broke his fall. For a RV roof with joist structure I wouldn't even count on that, dropping 2-3 feet after going through the skin might be enough to take out a joist.

Means you do not have a walk on roof. You will fall through the roof if you do not follow the owners manual.

Not all roofs are made to walk on, saves weight.

I'd suggest to follow the mfg's directions and cover it with plywood before standing on the roof.