Well not necessarily a historian but I am a Copt with a particularly large amount of knowledge of our history so I feel somewhat qualified to go into depth here.

Short Answer: Yes, many facets of Ancient Egyptian culture and religion were inevitably carried over into the Coptic era, in the form of afterlife, the initial Coptic cross, and even religious rites such as burial.

To give an example of an enduring practice that remains easily recognizable I named burial as it’s easily the most visible and easily recognizable constant. Ancient Egyptian religion believed that mummification and he associated rites would allow one to enter the afterlife and the trinkets left behind would serve as sustenance for them. Mummification did not necessarily retain these meanings in the Coptic Era... however it is still existed... which alone is a feat. Not just as some pagan practice that the peasantry held on to... but arguably as a religious tenet for many in the early church... to give a famous example St. Mark the Apostle was mummified in Egypt and buried, hundreds of other layman have been discovered mummified and among the last mummies we’ve ever found in the 7-8th Centuries were discovered on Monastary grounds. Mummification, arguably one of the most recognizable tenets of the Ancient Egyptian religion, survived for over 7-8 centuries as a sanctioned form of burial by the church. However even after it’s use subsided it left behind culturally ingrained fragments... such as the 40 day passing. Mummification was typically a 40 day long process... and so while burial is immediately after death... the last rites of the church occur 40 days after death and the family is expected to remain in intense mourning for all forty days, dressing only in black. At the end of the forty days a ceremony occurs to commemorate the dead.

Another easily visible element in the Coptic religion is Sham enNessim, or in Coptic: ϣⲱⲙ ⲛ̀ⲛⲓⲥⲓⲙ (Shom Ennessim) a festival celebrated by both Egyptians and Muslims as a sort of ‘Beginning of Spring festival’ which is no surprise as the event... and it’s name itself all originate from the Festuval of Shemu (The God of Harvest). You can celebrate this day as well when you visit Egypt, traditionally you’re expected to go outside a lot and go to the Nile at least once in the day. For dinner you must eat Fesikh (even if I personally don’t like it....) which has been eaten for the festival since pre Christian times. It’s been celebrated since at least 2700 BC and theirs no sign of this enduring holiday ever vanishing anytime soon.

On a related note the Calendar of the Coptic Church itself uses the old Ancient Egyptian calendar with a single modification of a leap year. The months are all organized into the same three seasons as the old calendar and every month has the same name. Which ironically means that the Coptic church officially recognizes the month of Thouth (Thoth) and Hator (Hathor) two Egyptian gods! While in the Ancient Egyptian religion the calendar played a large role, with the Sothic cycle (The rise of the star Sirius in the sky) occurring every 1461 years and played an important part of the religion. It holds little religious significance today however the fact that it has endured and also remains largely in use across many farming communities to this day is a testament to its preservation.

I could continue on and discuss how the Coptic vision of the afterlife (Amenti) differs slightly from the traditional ‘Hades’ of other forms of Christianity (River of Fire is a good example...) however I want to turn from Official Church Doctrine to popular practice among the people... who unsurprisingly didn’t just abondon their gods totally after converting to Christianity. Most remarkably the Peasantry managed to persist in a long and advanced method of spellcrafting and magical papyri under the Coptic church that lasted until the 11th-12th centuries (We get bilingual Arabic and Coptic magical papyri near the end). These papyri often mention gods like Osiris and Isis and usually mix them with other Judeo-Christian beings and demons etc.

To answer the final question: Yes Egyptian Paganism existed in some form by the time of Christianity. Alas it was ailing heavily from Greek and Roman influence. Temples were bankrupted by Roman policy and the Roman Assassination of the last High Priest of Amun in 27 BC weakened its authority in the state... not to mention the traditional head of the nation the Pharoah didn’t really exist and the people who were supposed to take the role (Roman Emperors) well didn’t. The religion was in shambles and so when Christianity came around it provided much needed stability and so spread relatively quickly when compared to other regions. It would have been a majority in Egypt by the 4th Century and by 450 AD if I remember correctly we get the last Heiroglyphic inscription as the practice died out. Their was certainly a 400 or so period where they coexisted however the Egyptian religion wasn’t exactly at its height at the time and it would be a poor comparison.