No, Chase points transfer as RDMs, not PQMs.
The Presidential Plus card (no longer accepting new customers) allows you to earn PQMs. However, the highest status you can achieve using those PQMs is Platinum.
You'd also still need to meet the 4 segment min and the PQD spending limits (waived for up to Platinum status if you also spend $25k on a MileagePlus Explorer card).