How appropriate is 现在是什么时间? for asking the time? 现在是什么时间?
  Now is what time?


This seems to be an alternative way of asking for the time in Chinese.  (The usual way is 现在几点了?)  However, something feels "off" about this question: I can only find it used in two situations, (a) when English is translated into Chinese, and (b) for questions such as:


  伦敦现在是什么时间?
  What time is it in London? (link)


Question: How appropriate is 现在是什么时间? for asking the time?
Both 现在是什么时间 and 现在几点了 mean the same. 

现在几点了 is used in casual situations. 

现在是什么时间 sounds that the speaker might think there would be something happening shortly or at certain time, so he/she wants to know the time. For example, 现在是什么时间？ 我们该上课了吧？

The effect is subtle. They can be used interchangeably.  But 什么时间 does sound the time seems more important. 

P.S. 现在是什么时间？ can also mean What time is it for? E.g. A: 现在是什么时间？ B: 现在是午饭时间/早操时间/自习时间/etc.