While it's always wisest to double check with the boss on the expectations - in most cases, yes, it's expected you'll have to take some time to set up benefits. In particular, I'd consider trying to navigate the trickiness of the administration and the benefits providers to be work time, although if you have a very complicated personal situation that requires intense research to figure out the right choice for your family, then you might consider that to be personal time.
Here's two examples:
Problem #1 - you have trouble logging into the benefits website, when you do, it's not configured with the benefits you were promised. After several calls with HR and the third party benefits provider, your benefits are still hopelessly screwed up, in fact they are extra-screwed-up because none of the "help" has actually been helpful. Solution - this is a work-time issue. Not only is the most help available during work hours, but this is all about navigating your employer's messed up system. Make sure you know the correct way to fill out any time reporting, and make sure your boss is in the loop about how messed up this stuff is - it's probably time to try outside channels because it just shouldn't be this hard, and your boss may even have additional resources. Given that benefits often have deadlines - you may also want to advise him of the urgency of this, and that you need to push NOW to get it done.
Problem #2 - the combination of family health issues, and your current living situation have made for a pretty complex mess. Any decision you make about health care providers could have a dramatic impact on the health of your family, and picking the wrong package could cause a financial nightmare in what is already a tenuous home situation. There's not any slack for mistakes this year in the family budget, so you need to spend a lot of time talking to your loved ones, making sure that critical areas are covered by your health care, and that the medical providers you depend on are covered in the plan you pick. HR and the benefit providers have been pretty helpful, but they can't make the decision for you - the bulk of the time is spent in conversations with family and doctors and surveying the finances. Picking the items in the forms will be easy when all of that's done. Solution: This is a harder one. Certainly time to research the benefits packages and the medical provider options is something you can do at work. But the long, difficult conversations about family objectives is not necessarily something you can ask work to pay for.
In most jobs, an employee comes to work pretty green. They don't have the access rights to half the techology, they have a lot to learn about how to do the job, there's all sorts of stuff that others have to configure for them. Usually benefits are among the first available things and the employee can figure that out in the first week or two while the real work stuff gets set up for them.
Sounds like in your job, because you were already familiar with the work, none of that is true and the push is on day one for you to be productive, and you can be... That doesn't mean that the benefits are unimportant, and I think you need to make it clear to your manager that this needs to be figured out.