Windows – How to increase the volume in the headphones past what is put out from the laptop

5.1 means "five loudspeakers and one subwoofer". As such, you can only use 5.1 sound if you actually connect five loudspeakers and one subwoofer. If you use those five loudspeakers and one subwoofer and position them according to the manual around your listening position, you will be able to hear sounds from all around you ("surround sound").
However, any 5.1 capable soundcard is also able to support any lesser configuration, i.e. Stereo/"2.0". The quality of sound is not affected by that, but of course two loudspeakers/headphones will not be able to produce sound that "comes from behind".

To answer your question: Yes, you can just use your normal headphones or laptop speakers. However, they will work in stereo configuration and will not produce surround sound.

(One exception: There is at least one sound card (Creative X-Fi) that is able to simulate surround sound using stereo headphones and some fancy signal processing.)

If your audio driver/software allows you to set discrete volume levels for headphones/headphone jack and in-built speakers, you can set the volume level for the latter as 0 or very low. That way, if the headphones get yanked out, the volume level should drop down to the one set for the speakers.