First thoughts on this as a player - I haven't tried to code anything like this for many years:
1. This wouldn't work on the edge of the board - which is where many life an death situations need to be resolved. One potential cutting point is all it needs for the eye to become false.
2. Linking two or more clusters via another cluster might be considered to render them equivalent to a single cluster. E.g. 3 clusters where 2 are linked would behave as 2 clusters. However, captures need to be considered - it might be possible to place stone in the region linking them, thereby capturing a cluster forming the link. Again, there are different considerations at the edge of the board.
3. A counter-example: 8 stones could be arranged to face each other on 4 sides and surround a box 2x2. If enemy stones surround 2 adjacent sides, and wedge in on the outside at the 3 points where the 2 sides join each other and the other 2 sides, the eye can be completely destroyed by the enemy placing a stone inside where the 2 sides join.
Have you considered the effect of enemy stones in the regions? Also, what about eyes that aren't completely closed off, so don't form a region?
Paul