Whether a presolver would eliminate the $y_k$ would depend on how the presolver was programmed. Assuming the variables survived presolve, giving the $y_k$ higher priority than the $x_i$ in branching would be similar to using a custom branching scheme in which early nodes are partitioned using $$\sum_{i\in H_k} x_i \ge 1$$ and $$\sum_{i\in H_k} x_i \le 0$$for some $k$. (I said "similar" rather than "identical" because I'm not sure all solvers would treat branching priorities as absolute, whereas you would presumably have full control over a custom branching scheme.)
Whether it would help is an empirical question. In a simple knapsack problem, I would be surprised if it did, but in a more complex model it perhaps might be productive if the variable sets were defined in such a way that knowing at least one $x_i$ took value 1 for $i\in H_k$ did something significant in reducing the solution space (tightened the bound significantly, forced other variables to be either 0 or 1, ...).
I have to disagree with the contention that the added binary variables and constraints "may result in loss of the optimal solution". At least as you implemented them in the example, the projection onto the $x$ space of the solution space of the expanded model is the same as the solution space of the original model.
