No, the Saleae software does not yet include a QSPI analyzer. It does include a 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 mean time, 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: 484165717