Q:

Do people "subvocalize" during thinking or "internal monologue"?

I've recently became aware of the concept of subvocalization, where people make tiny motions with their vocal cords when reading. I'm looking for a clarification on the subject:
Does subvocalization only take place when reading, or does it take place during thinking too? 
I found a some articles on the subject of detection of subvocalization

Modern technology can detect the small movements made during
  subvocalization by monitoring electrical impulses. As of 2011, the
  National Aeronautics and Space Administration (NASA) is working on
  technology to detect these forms of silent speech. By reading these
  faint electrical impulses that occur during the process of
  subvocalization, machines could appear to read a person's mind and
  respond seemingly without the person saying anything. All the person
  would need to do is clearly think the command he wants the machine to
  carry out.

The last statement makes it seem as if subvocalization can be detected during thought.

A:

Short answer
Sub-vocalization can also be detected during cognitive demanding tasks other than reading.
Background
As far as I can see, most literature acknowledges sub-vocalizing as being only detectable by measuring the electrical nerve activity that drive the speech organs (e.g., Parnin (2011) and NASA Research). When people perform complex tasks, these sub-vocal utterances can be recorded as electrical signals sent to the tongue, lips, or vocal cords, and these can be detected. 
Sub-vocalizing has been mostly described in terms of reading (e.g. Slowiaczek & Clifton, 1980). Nonetheless, more recent literature also associates and acknowledges sub-vocalization when people perform mental tasks that claim a lot of mental processing, such as software programming (e.g., Parnin (2011), so the answer to your question is yes, it also occurs during thinking.
Interestingly, as a side note, stutterers sub vocalize more slowly, reflecting the fact that indeed much of the same mechanisms are at work during sub-vocalization as during normal speech (Bosshardt, 1990). 
References
- Bosshardt, J Speech Hear Res (1990); 33(4): 776-85
- Parnin, IEEE 19th International Conference on Program Comprehension (2011)
- J Verbal Learning Verbal Behav (1980); 19(5): 573-82

