There is no way to specifically turn the dimension off as it is part of the Offset Relationship that is created by the command, but if you turn off Maintain Relationships, then it will not create the Offset Relationship and thus the dimension.
I think this 'feature' highlights some of SolidEdge's inconsitensies/quirks.
By that, this is what I mean....
whilst 'maintain relationships' is turned on, the dimensions for offset will appear, but other dimensions (which are also locked) will not appear automatically, such as that of Ø of circles, or length of lines. One can ofcourse select the 'automatically create dimensions for new geometry' from the intelliSketch options, and that will display dimensions as elements are drawn.
Though I don't know why turning off that option does not affect the offset feature same as creating other elements...
Ironing out inconsistensies such as these, I think will make using ST7 a much more enjoyable experience.