The only issue you'll encounter when changing Publication relationships are possibly naming conflicts (i.e. if an item has the same WebDAV url as another). This isn't a problem with new Publications "in-between" an existing pair of parent-child Publications.
As for why you're creating this setup, Publications for what we typically use Target Types (Purposes) is not typical for BluePrinting. I have seen this somewhat fit one use case (see this post) for a long term review scenario at one customer (which they did not implement).
The biggest challenge would be "merging" changes across the Live Publication, PreLive Publication, and Preview Publication. In typical setups, you have a single source for content where this isn't a problem. With this BluePrinting hack you want to be sure the inheritance is correct or you have a way to move localized changes to their sources in the BluePrint.
With Live as the lowest child, unlocalizing would be a way to accept changes for the site. Again, I don't know what this is like in practice, but I would not recommend it as a best practice or first choice without more context on what you're trying to do.