There's only way to find out. The mistake would be to bring him in, because of his draft status, without competing.
Rush has earned his position on the roster, so I wouldn't be in too much of a hurry to replace him unless someone beats him out for the job.
Depends how Cowboys brass view and consider Willis as a prospect and developmental player, imo.
Would be more competition vs Wil Grier as the 3rd QB, than Rush who apparently still has McCarthy/Schott team impressed.
We did not draft a mid to late round developmental QB, nor did we bring in any familiar name undrafted rookie QB.
So this leads me to believe that it will be the current status quo with Rush, Grier - this team does not have backup competition nor immediate development
high on their priority.