I'm not sure if the particular task is unconventional, but I'm certainly impressed that they acknowledged the use of the internet even if in doing so giving that option a handicap.
Is there some merit to this strategy of "help+limited time" vs "no
It's difficult to guess what they are getting out of this. They may put more stock in one option over the other, or they may be examining soft skills that come as the result of choosing either option.
If it was myself I'd rather see someone understand that they sometimes need to ask the right questions; whether those questions be to google, people in the office, or to the rubber duck on their desk I don't think it matters.
Does the choice I make tell them something about my coding skill or
Unfortunately sometimes it's difficult to guess what the interviewer is really after, they likely have some metrics that they will get from that particular task, but it could range from your reaction to being given the option in the first place, to what you googled. Very difficult to actually know for sure.
As per the comment below lets have a stab at looking into what they could be concluding from the task.
The choice Itself:
This could show them that you're aware using resources readily available to you such as the internet can help solve a problem quicker.
The opposite is also true, they could take it that you're showing that you are unfamiliar with that particular technology, concept and or problem.
The Task itself:
This could allow for some more assessment stemming from your initial choice. For example, you've opted to use the internet as a resource; are there elements within the task that are considered core concepts of the language and or technologies that they are using, and as such maybe they believe not knowing these without the use of a resource like the internet is a negative.