Is it possible to output audio from the speakers while a Bluetooth headset is connected? In iOS, this is achieved by double-tapping the home button, swiping right twice, and selecting the speakers.

Can this be done in Android?
You can accomplish this by disconnecting the stereo audio (A2DP) profile from your headset. This still keeps your headset paired with the hands-free profile.

You can do this by opening Bluetooth settings, long-pressing your attached device and unchecking Stereo audio.