I know the "Is X a Timelord" discussion gets a bit old, but I think we should come up with a consistent scheme.
As far as I know the first question of this kind was asked by TangoOversway:
Which has received a score of +34-6 (as of this writing) and was not closed.
However, similar questions asking if some fictional character that exhibits any similarity with The Doctor could be a Timelord are typically closed. I know there were some of these questions in the past, but I cannot find them right now (maybe they were even deleted after being closed). The most recent question
Was closed as not constructive with a score of +3-3. From the original question that remained open for about a year now (it was never closed/reopened), it would appear that the community considers the question valid, although there is barely any qualitative difference between these questions.
There have been two claims that were supposed to be an argument why the latter should be closed and the former be left open:
"Santa Claus appeared on DW while James Bond did not. "
- a) incorrect, as James Bond has been mentioned several times in DW episodes, and
- b) actually irrelevant as it would be part of a potential answer, not legitimation for closing the question.
"The Santa questions asks in Universe for the Santa that appeared on-screen."
That is incorrect; The question text doesn't even mention that Santa had an on-screen appearance and even remarks
His appearance changes from movie to movie, indicating he might undergo regenerations between movies.
which indicates that it is actually asking about the general figure of Santa Clause as it appears on various media, including but not limited to DW (note that there was only one DW film).
By this reasoning, the questions are equivalent and either all such questions asking if a figure that exists outside the DW universe is a Timelord should be closed or all should be okay (within reason; some argument for the potential validity of the claim must always be provided).