Could a Codex Compliant Chapter of Space Marine stay hidden while continuosly operating for 10k years?

I was discussing the lore of my Homebrew My Guys chapter, and due to their 30k origin and genetic taint I imagined them as being rather shy, conceiling their existence from the wider imperium, pretending to be one chapter in one segment and another one in the next

Does this make any sense? Is It plausible? Can they escape the gene seed tithe to Mars? Can they get equipment like Terminator Armor by producing It in house or by bribing a forge world? Can't wait to hear your thoughts.