Will the installation work if you are building brand new sites on localhost, or on a temporary server where the domains are not propagated?

For instance if I install a new site on my Cpanel Server I can get to it by going to servername.com/~tempsite which is the working directory until I were to actually change the DNS on the domain to point to it, then it would work normally, but obvously I can't have visitors looking at my site AS i'm building it, so ....

Will Multi sites work this way, or do the domains HAVE to be fully propagated?

To use JMS on a localhost, see the user manual chapter 9 that explain how to simulate the DNS to have the correct domain name.
You have to use the _host_ parameter where you set the domain that you want to simulate.
Becaurefull that none of the slave site definition can have the localhost/... This is forbidden because in this case, the _host_ is not read.

You can try using a temporary path in the URL but this is not recommended.
It is better to use a subdomain of a public domain to make the test.
In general, I recommend to use a speicific domain for the registration of the cPanel server and never use a public domain. Just a domain for the server.
So that, you can easily move from one server to another one and you are not binded to this domain name and you can use subdomain to simulate the future Addon domain that you will create for the target. Remember that an AddOn domain automatically a subdomain on your primary domain and therefore that is very easy to simulate and test the website.

It is not required to propagate the DNS as long as you can access you new server with a domain name.

Follow our architecture recommandation present in tutorial video 0.b slide 21-24
So that you can easily move your environemnt from one server to another one and it will become also very easy to have a single linux shellscript to performa a backup of everything in one shoot.