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It's possible to switch between listening for BLE advertisements and perform a WiFi data transaction for CYW4343W. Please check the document in the link : 43xxx_Wi-Fi/doc/WICED-BLE-WiFi-Introducer.pdf which is similar to your implementation and may be helpful.
Also, there would be overlapping of the spectrums for the radio and you have to enable coexistence to avoid interference.
Please note that default implementation for the CYW4343W chip is TDM type coexistence.
Kindly go through the below application note and blog post regarding coexistence interference.
AN214852 - Collaborative Coexistence Interface Between Cypress-to-Cypress Solutions and Cypress-to-third-party Chips