No. A filed case and a paid US$15,000 fee create a pending matter, not a status and not work permission. Entry as a permanent resident still requires eligibility, admissibility and an available immigrant visa. Any earlier trip would need its own valid basis, judged separately by the officer at admission.
Assess an earlier trip under its actual admission category
A twelve-month lease does not create permission to enter, and a pending immigrant case may be relevant when an officer assesses a proposed temporary trip. Describe the actual purpose and intended activities truthfully. If the family plans to relocate permanently, do not treat visitor admission as an automatic bridge to that move; obtain advice on the basis appropriate to the real plan.
If a question is not answered there, the honest position is that it is unresolved, not that it works the way some other category works. The case uses classification under either EB-1 or EB-2, subject to eligibility, admissibility, and visa availability.