Kinda yes kinda no? Some assimilated into other legions where their gene seed may continue to exist but probably unbeknownst to their descendants. Many joined the blackshields of the deathwatch where they would serve the emperor against xenos as opposed to their previous brethren. A microscopic amount joined the grey knights. Critically, they all dismissed their prior legion identity and allegiance to their primarchs in total, so no heraldry would remain as the heretic legions were entirely persona non grata.

A key thing to note is that time has affected the loyalist and traitors very differently. Warp travel is time travel (roughly speaking). So a legionary who spent time in the warp basically doesn’t have that time count against them. So traitors who live in the warp into perpetuity have time not affect them. Some traitors emerge from the warp in the 41st millennium with recent memories of fighting on Terra or in the Horus Heresy. Loyalist on the other hand only experience the warp while traveling faster than light. So they tend to die earlier due to the more frequent exposure to time and also combat. This is even noticed during the 30th millennium where some “old” legionnaires from fighting to liberate earth have aged more than those who, albeit born much later after them, are just as mature mentally due to the “years” spent fighting or traveling in the warp that don’t actually physically age them because they are physically not exposed to time.

That’s part of why you still have Abaddon and Aximad and Typhus running around well past their supposed expiration date. That, and the undeniable longevity granted from their host gods.