It may be best to set a building option to be shown for that custom drawing mode. Then, when in a plan set you can use custom visibilities. You'll still want to be sure to have that building option on only when drawing those dimensions though.
Or, (even though dimensions and notes typically only show in their respective modes) as I do for floor, ceiling, or roof mode, I have all the stuff I only want to show up in those modes set to a layer that is the layer drawn on in those modes. For instance, in roof mode I have a "roof only" layer. That layer is set as the active layer when I switch to roof mode. That way if I draw a shape, note, dimension or anything else, it is on that layer. Then, that layer is only set to be visible while in that mode (unless I want to check something). It gives an added control for visibility.
I use a more complicated set up with some commercial projects. When I do tenant finish spaces I have all the walls and basic elements of the building and the interiors on the default layers and default building option. But, the information that is only needed for each tenant space is on a group of building options set for that space. Only thing is I have to remember to keep those things in their proper building option. But, when I do follow that method it is easy to turn on and off building options to see each tenant space's unique information.