This is an interesting idea, and while I'm sure people are tired of us EVE Online vets making comparisons between that and Starmade, it would be possible to run several servers each with jurisdiction over a specific galaxy, much like Tranquility which is the supercomputer cluster of blade servers CCP Games uses to house the EVE universe and all of the magnificent bastards that call it home. (For those unfamiliar with how EVE servers work - its all the same interconnected universe, but different servers host different systems and so shit going down in Fountain won't necessarily affect Catch since the two regions are on different server clusters)This would mean larger scale, and larger server population, all without impacting server performance.
However, while a system like this already works in the case of EVE we have another problem to deal with; that is, all of the EVE servers are owned, controlled, and administrated by CCP, and with a few exceptions are all practically in the same room of the same building in Rejkavik. Starmade's servers, on the other hand, are independently owned and operated. This creates a bit of a problem as people have mentioned before, because if you're going to allow intergalactic travel, the source and destination servers need to be similar to each other. Now settings that have an impact on server performance but not necessarily game balance can be ignored - if server B can handle larger planets than server A then there isn't any reason why server B's planets should be constrained to match server A - but things such as balance tweaks, starting equipment, mining bonuses, etc. need to be the same to keep gameplay fair and balanced. And player information needs to be, if not shared, at the very least synchronized, because the idea isn't just seamlessly changing servers, you're also bringing character and faction ID, inventory, and whatever you are currently flying with you.
Now all of this would be easy if the servers were all owned and administrated by the same entities, but we've got many, MANY different servers all franchised with their own admins, data, and rules. If something like this is going to work it needs to be either A) multiple servers owned and operated by the same people, or B) a joint, cooperative effort between the admins on two separate servers, because though you might have two different machines in two different geographical locations, the only way to allow this while keeping gameplay balanced is to essentially merge the administrators of those servers into one allied group.
I'm all for it - I think having interconnected servers will do wonders for allowing larger-scale games with larger numbers of players, and it solves the ever present issue of server performance at least on the grand scale - though if an entire fleet from server B wants to all go play on server A at once, that could be problematic. But any kind of interdimensional travel of this sort will only work if the gods of each universe (read: admins) are willing to allow it and can actually agree to work together, let alone come up with a shared rules standard, rather than making it a dick-measuring contest on a multiversal scale like some people (and I shan't name names -_-)