>Yes, it would work. However, when I compile my classes into COM dlls, for some reason I often cannot access objects added on the fly. Only objects that are part of the DEFINE CLASS statement are exposed. I do not know why.

Hmm, did not ever tested such thing. However, I suppose that working with COM objects cause that. Say, you have COM object that expose its methods and properties. When you add object at run-time, it just added in the scope of 'inside' of COM object. 'Outside' of COM object noone can see it because that new object was not declared befor compiling, so it is not in COM object interface. That is why you do not see it.
Yes, making it at design-time will solve this.

>But it is weird that as it is possible in source code, they should have allowed us to add objects to custom classes also.

You may try to use container base class for main COM object.
Yes, it is weird, same as grid headers and columns. Header may be subclassed, may be put into VCX and than used in desighn-time to drop such new header class into grid columns. But still you cannot make header class using class designer, and cannot edit it in designer. With columns - better do not deal with their sub-classing...