For all intents and purposes, not-fatal injuries directly caused by a demon may heal a little faster than normal, thanks to the demons' influence. You won't be good as new immediately, but characters won't be slowly bleeding out or immobile if they refuse all medical interference due to an effect taking hold. The body may also just push straight through the pain, due to the demon's effects taking hold, so once it's over with, the character will still have their injuries to deal with.
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For all intents and purposes, not-fatal injuries directly caused by a demon may heal a little faster than normal, thanks to the demons' influence. You won't be good as new immediately, but characters won't be slowly bleeding out or immobile if they refuse all medical interference due to an effect taking hold. The body may also just push straight through the pain, due to the demon's effects taking hold, so once it's over with, the character will still have their injuries to deal with.