Basically yes, that Egypt was united again. It's not as arbitrary as enough time having passed for a new Kingdom.

The period that the Hyksos ruled is what we call an intermediate period. An intermediate period is a shorthand which is useful for an historian but does little justice to the complicated political dynamics that occur within that timeframe. But anyway, these intermediate periods come between the Old, Middle and New 'Kingdoms'. A 'kingdom' period is one where Upper (South) and Lower (North) Egypt are united. So, intermediate periods are those where Egypt is split in two (or sometimes even more). In the 2nd intermediate period, the Hyksos ruled Lower Egypt in the north, while other dynasties controlled the south. The southern native Egyptian dynasty was living fairly peacefully with the Hyksos until Kamose started (or continued) a successful campaign against them. But he didn't quite make it all the way to Avaris, their capital, so he was only ever king of Upper Egypt (see Ryholt, particularly 172-4). It was Ahmose who completed this campaign to fully expel the Hyksos, uniting Egypt again and thus starting what we call the New Kingdom (another useful but limiting shorthand). Sources: mostly Ryholt