I will be getting married this Tuesday and will be getting off-post housing. Will NCOs be able to inspect, like in the barracks?

Yes NCO's will be able to inspect your home off post. Most likely they won't unless you ask them to look at your home before you sign the lease.

I can't say on Army based stuff but I know within the Navy world, that you can be inspected but it's only due to some speculation. They are not random. When I lived in military housing for almost 2 years, I never got inspected (from what I know). You just have the basic before you move in inspection done by you to check for any issues with the place and then when you leave when they come and check to see what damage ya'll have done. It's no big deal.

They can come see it but not in the same way as inspecting your barracks.

During my 14 years in the Air Force I only made one check off base and that was because I was told that he was having problems at home and didn't have a car that day. After bringing him on base military police detained him until the local police showed up and took him away for raping a minor. looking back I was really there to make sure he was away from the house so they could get his family out since he has a 3 year old daughter and so they could gather evidence.

Living off base is nothing like the barracks, as long as there is no worry about suicide you basically will only see someone from your unit if you invite them over for a party or to hang out.

No.

Yes, they can. If it's military housing, the Housing Officer can inspect it anytime, or give maintenance crews the key--and they might accidentally open the door while you and your new wife are busy on the couch. True stories.

In a word, no. However, that is not to say your Sgt won't come by for a cup of joe or just a little chat. It may just be to know how to get to your place in case of a comm-out recall (used to do them all the time, had to know where my people lived). Be sure your new spouse knows where things are on post and who she can call if she has questions, trust me, she will.

In my 21 yrs in the army I never had any one come to my quarters or off post housing and as an NCO I never had a reason to do that either.

No they won't inspect your place but they can require you to bring in your uniforms and also inspect your
All your field gear TA 50.

At the end of the day yes they can but a memorandum needs to be signed allowing permission, now with that being said as you've seen several others say come to work on time, and don't give them a reason to want to check and you'll be fine.