Hello, dear friend,
yes, it is possible to make this as an adaptive component family. But the family will be quite "heavy", and when you place a lot of instances to the host model, the performance of the model could be decreased significantly.
And what do you mean by "adaptive"? Adaptive will allow you to resize your family, but you still will have 7x7 rectangles (not squares then). Also, you can create a family, which automatically adds needed squares (when you change sizes), but this will make your family more "heavy".
Maybe a simple non-parametrized generic face-based family will help you? Almost the same problem discussed in this topic.
And maybe you can show the ornament as an ordinary hatch/decal:
1) you can try to create a very simplified ornamentation in pat-file manually (google it, there are a lot of instructions how to make a hatch by means only the notepad),
2) or you can use a picture and place it on a model element as a decal,
3) or you can use special plug-ins for custom hatches (maybe there are some hatches like to arabesc) — hatchkit and so on, search in the autodesk exchange.
