Can I replicate to a pre-existing database? I am going to test this out, however I'd like to know what the forum would say.

I have 2 SQL servers with replication setup between them.

I am now adding another new SQL Server and I want this one to be the new publisher. 

Do I need to recreate the databases on the old server when I setup replication again? 

Can I simply stop subscription and then begin replicating from the new server to the same databases after I setup the machine?
Yes. After dropping the subscription, you will be able to simply configure replication from the new publisher to the existing subscriber. There is no need to drop the subscriber DB. Please bare in mind however that the subscriber will need to be re-initialized from the new publication. (Assuming transactional or merge publication) this can be achieved either through the snapshot agent or a backup/restore. 

Also bare in mind that assuming your new publisher will also be your new distributor, you will need to configure this as well.