here) and the Danellians/Time Patrol timeline (see here) are incompatible. For example, the Technic History has no New Edom on Mars or Second Asteroid War in the 29th century. It has no Martian War or Guidance Corps on Earth in 3890.
However, might these two universes coexist in a single multiverse? There is one piece of evidence:
Nicholas van Rijn exists in the Technic History;
Sherlock Holmes exists in the Time Patrol timeline;
both men visit the Old Phoenix Inn between universes.
This evidence is not conclusive. There may be different versions of Holmes. In fact, there are different versions in films, on TV and in books by other authors. Nevertheless, we might provisionally assume an identity between the Holmes encountered by Manse Everard and the equally authentic seeming Holmes seen by Valeria Matuchek.