. . . since this is a Microsoft Account with the password not saved locally.
Just as a side note, this is not correct. Microsoft Accounts absolutely do have a local copy of the password saved (encrypted, of course), or else it would not be possible to log in without an active internet connection to verify the password, and you can.
It's simple enough to prove this to yourself. Using a Microsoft Account that's under your control, change its password on the Microsoft.com website. Verify it's been changed by logging out and logging in on Microsoft.com again. Now log out on your Windows 10 machine where you're using he Microsoft Account linked Win10 user account. Now, log back in on the machine, but DO NOT use the new password you just reset on Microsoft.com, but your old one. You will succeed in logging in. You will succeed in logging in for months on end with the old password provided you DO NOT, even once, use the new password, but only the old one.
On login on the Win10 machine, if you supply the correct password that's stored locally, no check of the cloud based password is done, because it's not necessary. But as soon as you enter something other than the locally stored password, a check of what's in the cloud for the Microsoft.com account linked to the user account occurs. If there's a match, you are logged in and the local copy of the existing password is replaced by what was on the cloud. If it's not a match to the cloud password, you can still get away with entering your old password, and it will work.
Microsoft was never going to design a password mechanism that required an active internet connection in order to log in. There are just too many reasons that could be absent when anyone happens to need to hop on to their machines.
All of the above being said is not a comment on whether PCUnlocker can deal with Microsoft Account linked Win10 user account passwords or not.