This is wrong. It does some verification at startup, but it's not the full chain, since reading 300+ gigabytes at every startup would be pretty slow.
I never said it verified the full chain. As far as I am aware, the full chain is only verified on initial download, if the user performs a reindex, or executes the
verifychain command starting from block 0.
Still, poking in to it a bit more, it seems
that Core now defaults to performing a level 3 check on only the last 6 blocks on start up, which is much fewer blocks than I thought it was. It used to be 288 blocks, but seems to have been reduced to only 6 many years ago.
However,
Andrew Chow points out here that Core still verifies the integrity of its databases on startup, so may detect a tampered block that way.
So to more fully answer OP's question, it depends on how far back the block he is editing is, and how exactly he edits it, whether or not Core would pick up that it had been edited outside of a full reindex or verifychain. Not that editing an old block would achieve anything, since it won't be broadcast and would be rejected as invalid by any other node anyway.