No, Wolfram|Alpha questions should be explicitly off-topic, regardless of whether W|A is being used through the web interface or Wolfram|Alpha Notebook.
Vote here if you agree (and post the opposite answer for voting, with appropriate arguments, if you disagree).
The interface is a minor detail that should not decide whether W|A is off-topic or not. It would be quite ridiculous to tell people: "Your questions about this W|A input is off-topic because you used the website. Had you downloaded the GUI and typed the input there, it would be on-topic."
As for asking about the GUI vs W|A input: as @MichaelE2 says, "I think the distinction @b3m2a1 makes might be hard to make in practice." I do not think most people who might post questions would be able to understand the distinction, unless they are also very familiar with Mathematica.
The reasons from https://mathematica.meta.stackexchange.com/a/267/12 still apply:
" I know that W|A runs on mma and it kinda sorta understands mma syntax. However, opening the door to such questions will only lower the bar and result in hit-and-run questions from folks who just want a quick result from W|A."
Having expertise in Mathematica / Wolfram Language (which is what users of this site have in common) does not translate to Wolfram|Alpha. While W|A understands some Mathematica-like input, it often interprets it differently from Mathematica. W|A does not have a documented syntax. Its understanding of natural language is constantly evolving and often unpredictable.
W|A (not W|A Notebook) has a much larger userbase than Mathematica, most of whom have no familiarity with Mathematica whatsoever, and would not fit in the current community. Additionally, there is good reason to suspect that many W|A questions would be of the hit-and-run type, coming from students looking for a quick answer or homework solution.
It is difficult to maintain a community like the one organized around Mathematica.SE. There are even concerns that things are not going as well as they used to. In my opinion, inviting W|A questions (which are orthogonal to Wolfram Language questions) will bring nothing of value to the community. In fact, I worry that it might even be the last straw that breaks the camel's back.
Note that there are already places for W|A questions: WebApps.SE and Wolfram Community. There is no pressing need to create another one.