To clarify, are you asking if it's possible to run the QFX session from within an application using the SDK without opening the Quick Fields program itself?

I had asked this question a number of years ago, and the answer was no.  Since that time, Laserfiche has rolled out Quick Fields Agent and Workflow, both of which would have resolved the process flow that I wanted to accomplish in my desire to open a quick fields session from the SDK.  Granted, depending on your platform/license these products are an additional cost.