In fact, I believe it is possible to post on a server to which you have an invite. The quoted post below explains.

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Quote:You can temporarily join a server through an invite link with what’s called an “unclaimed account”. This is a temporary, shallow account, and its purpose is just to let you operate on that server for however long you happen to stay.

With this unclaimed account, you can operate normally, sending messages in servers, sending DMs, joining VCs, sending and accepting friend requests, and even creating and managing your own server. One thing you can’t do with this account is purchase or gift Nitro subscriptions.

The main catch with this account is that once you log out, there’s no way for you to get back in (closing the tab or the app doesn’t count as logging out). When this happens, your messages, friendships, servers, etc. will remain, at least for a while, but you will have no way to get back to this account.

If you want to be able to get back this account after logging out, you can simply claim the account by going to your account settings and adding an email or clicking “Claim Account”. This process will be as easy as creating a fresh account.