Even if Egypt "falls", it will recover in a changed form, as the Levantine states (except Ugarit) mostly did, even if with different ethnic identities (and it took a while; Egypt's recovery would be faster since the land is inherently more productive, allowing quicker accumulation of surpluses).
While the New Kingdom survived the Bronze Age Collapse (albeit in a reduced form) shortly thereafter you have the so-called Third Intermediate Period, a long phase of weakness, division and what can be construed as foreign domination (25th dynasty and what happened after that, though whether it counts as a part of the Third Intermediate is debatable). However, it seems hard to reduce Egypt to a state similar to post-Hittite Anatolia, for example, for clear demographic and geographical reasons. The Saite dynasty seems to be when Egypt came back to her past glories, but even then, it hardly ever returned to something approaching the Late Bronze heights of the 18th and 19th dynasties (and one could say it would never happen again until the Ayyubid/Mamluk periods millennia later, except for a short Ptolemaic phase at the heyday). Even the Saite zenith, however, would prove fairly short lived.
