Some positions get designated essential not because day to day operations require that a shop be open at all times, but because if something goes wrong the powers that be want someone on hand, right now, to deal with it.
If that is the reason a shop has designated essential positions, it's entirely possible that you have very little high-priority work to do during the government shutdown. Your boss probably knows this too.
As a new employee in government, it is likely that there are reams of policy and guidelines that impact your work that you have never read. Or maybe there is some low-priority project that isn't normally allocated resources. Talk to your boss about one of these. Either is a productive thing that you can do, and keeps you available in case the batphone rings.
That said, to your questions:
Is this option worth taking?
If you really value the possibility of free time off, then it might be.
Are there any possible repercussions (career wise) from getting furloughed? Will it look bad for a new employee to be "wanting out"?
- A non-essential position is more likely to be cut for cost savings than an essential one.
- If you and your boss both know that you have no high-priority work to do right now, and you and your boss both know that you could be making productive use of your time, then your boss will probably think less of you if you ask to be furloughed.
- If there is literally nothing for you to do in your job description, see if your boss wants to loan you to another team. This would expose you to other aspects of your organization, and give valuable experience that would make you a more valuable employee.
- If your boss isn't jaded about working for the public service (i.e. still thinks it is a good thing to do, rather than just a job with a pension), and thinks you are asking to be furloughed so that you can have free time off, he will probably be very displeased, even if he doesn't express it to you directly.