Just wonder what if my mail server went offline for some periods, and the sending party couldn't deliver.
Will there be any consequences except I don't get the mail? I tried searching but they all in the perspective of a sender and get a bounce, rather the other way around.
Unless something has changed massively since I was deeply involved with this stuff, the people that sent you email may get a notification after some hours that their message is being delayed, and maybe after like 24-48 hours they might get a bounce. But if it’s just your SMTP server going down for an hour or two every now and then, the system should be able handle that seamlessly (barring some hiccups like messages showing up with timestamps hours in the past which sometimes is confusing).
The problem with this is the probability of your server being available for the next retry is fairly low.
Usually some sort of exponential backoff is used so it might retry after 5 minutes, 15 minutes, an hour, 3 hours, 6 hours, 24 hours, 48 hours, give up.
6-8 hours is probably too much for anything serious where you don't want emails to just drop. It will work so if you're just using it to sign up to sites and stuff, you can make sure your server is on to receive the verification emails and stuff. But I wouldn't use it for anything important.
I think 8 hours starts to get into territory where they might get an informational message about the delay? That also starts to be long enough that the emails might get lost in the distant past in the client and never be seen, by the time they arrive.
I think when I used to do this, it was one advisory message every 24 hours that a message was holding in the queue, and after 5 days it would bounce, but I have to assume that those limits have shrunk in the modern day. How much, IDK; it might be worth experimenting with it though before committing to creating that situation since it might not go okay.
If you're concerned about missing emails, you might want to sign up for a forwarder instead. I don't see the point of running an email server that's going to be off for long periods of time.
Generally it's not going to put you on a blacklist if a sending server doesn't manage to send, but some have very short queue times before they'll drop it, so you're going to miss a lot of mail that way.