You can enter the Alhambra grounds and see other areas before your Nasrid Palaces entry time, but one hour will be insufficient to do so; unless you aren't much interested in anything other than the palaces, you'll need some additional time after you finish at the palaces to see other parts of the complex if you only arrive an hour early. Also allow time to pick up an audio guide if you want one. In addition, I'd suggest stopping by the information counter at the visitor center to get the day's schedule for the various building in the complex. Not all are open every day, and the hours vary. It's possible that something you want to see will close at 1 or 2 PM, for example.
When I visited to the Alhambra in 2019, there was a queueing area for those with the next entry time. There didn't seem to be any real advantage to being at the front of the line for the entry time, because all the other folks with the same entry time would be right on your heels. Perhaps if you really needed to rush through the Nasrid Palaces and weren't going to take any pictures, you might benefit from being at the front of the line.
At most of Europe's popular sites, the early entry times are very busy. I'm not sure why, but I think a lot of tour groups like to get the biggies out of the way early. But in the case of the Alhambra, there's a good chance it will be sold out for all entry periods anyway.
Keep in mind that there are a few spots--including the Nasrid Palaces--that can be entered only one time. One of the other such places is the Charles V Palace, which now includes a museum. I'd recommend not entering that building shortly before you're due at the Nasrid Palaces, because you won't be able to return later to finish seeing it.
I think you'll find the early entry times at the Alhambra sell out first, so if you want to see the Nasrid Palaces early, you're probably smart to buy those tickets early.