No, the Saleae software does not yet include a QSPI analyzer. It does include an SPI analyzer as well as a synchronous parallel analyzer that could be configured to operate in a 4-bit mode, but it will not automatically combine the 4-bit nibbles into 8-bit bytes.
We plan to support QSPI in the future but don't currently have it on the road map. In the meantime, if you are interested in developing a custom protocol analyzer, you can find details here: Protocol Analyzer SDK
And you can find the supported protocols list here: What protocols are supported?
trello ID: 55f751cba762758db28b6173
trello data: -1798988255