Will a site proposal that covers a subset of Stack Overflow work?
Depends, but it can work. We have a precedent. Mathematica.SE. As I've explained here, it worked (even though it was a complete subset), because the MMA community on SO lived in the walled garden of the mathematica tag. They didn't use the rest of SO, and, vice versa. So, when they "voted themselves off the island", it didn't affect SO, nor did it affect their own community.
On the other hand, a site like TheoreticalPhysics.SE (which was a full subset of Physics.SE), will fail because the community on Physics.SE didn't migrate over. Most just straddled the gap, but didn't contribute much to TP.SE due to lack of questions. In the end, this was due to there being no definite separation between the TP and non-TP community on Physics.SE.
With respect to SO, Arduino.SE seems to be more like Mathematica -- a niche, "walled garden" community. As I've mentioned in that post, however, it seems to be more like TP when we compare it with EE. But that's a separate matter here.
What will be the pros and cons of making Arduino off-topic on Stack Overflow?
You won't. The existence/non existence of another site doesn't affect the topicality of a question on a certain site. Scope doesn't change unless you meta post about it and ask for it to be changed.