If a computer is in AD but has never been turned on, will it show up in the database?
No
Another question I have is, if I click delete permanently but want those computers to come back into the database, will they? or do they get flagged somewhere to be ignored?
They will come back, if you don't want them to come back you can add them into the "scanning exclusion" list
I am currently missing some computers from the database that exist in AD, one is on and running (I deleted it a while back) and the others haven't been turned on. I need them all in there.
If you use active scanning they will show up as soon as they contact a domain controller.
Or if they are turned on you can do a lsclient or lstrigger on them.