Will generic earphones allow basic inline remote / mic capability on my iPhone 6? I'm interested in buying the Sony XBAA1AP earphones, and am curious if earphones that aren't specifically designed for iPhones, but which have an inline remote control / mic, will provide basic remote control / mic features on iPhone devices.
Yes, generic earphones/headphones/earpods will work fine with an iPhone.  I have several non-Apple headphones and earphones from various manufacturers and they've all worked, including the play/pause, ff/rw, volume buttons.

As long as you purchase from a reputable company and manufacturer, like you've indicated in your question, you'll be ok.