Let's say Constantine dies in the early 1000s, for the sake of Basil having an adult son or grand-nephew at the time he dies (it seems sixteen is old enough to rule without a regent, on the outside edges, and Zoe is probably going to be able to bear a son up to at least 1009).
Basil is not known for being willing to share power, or trusting others in general. I'm not sure he's going to pick someone like Constantine Dalassenos (a competent and strong willed sounding option, but problematic as far as the reigning Emperor goes precisely for that reason) instead of Zoe's OTL husbands, and if he marries I have a time time imagining him being comfortable associating his son with government, or a man of his temperament being a positive influence on a son. Cold, harsh autocrats have an awful track record here.
I'm sure one could write something where Basil does indeed have a qualified successor and the Macedonian dynasty continues, but those would be my personal thoughts as far as likely as opposed to just "possible".