Can PostgreSQL databases be attached/detached on the fly?
No, short answer is no. This has been asked at the PostgreSQL development mailing list at 2011: Detach/attach database
 and the many replies in summary said "yes, this is feasible to implement but quite complicated to do so.":


  You would have to do quite some surgery because of oids from shared tables. I don't think thats easily doable.  
  
  Andres Freund
  
  
  
  The main reason this doesn't work is XID management.
  It's barely possible you could make it work if you first locked all
  other sessions out of the DB and then froze every XID in the database,
  but that's a sufficiently heavyweight operation to make it of dubious
  value.
  ...  
  
  Tom Lane
  
  
  
  I have to admit I've thought about this from time to time, and it
  would be pretty cool.  I was initially thinking that it wouldn't be
  that difficult to do this on a per-database level, because if you
  slurp up a whole database then by definition you're also including the
  system catalogs, which means that you have the pg_class, pg_attribute,
  and pg_type entries that are necessary to interpret the table
  contents.  If you do anything more fine-grained (per-tablespace,
  per-table, or whatever) then things get much more complex, but at the
  database level you only need to worry about interactions with other
  globals: tablespace and role definitions.  And we could probably write
  code to grovel through the system catalogs for a newly "mounted"
  database and do search and replace on the appropriate columns, to map
  from the old OIDs to the new ones.  It wouldn't be simple, but I think
  it could be done.
  
  But Tom's point about XIDs and LSNs seems like it kind of puts a
  bullet through the heart of the whole idea.  Now, before you can move
  the database (or table, or whatever) between clusters, you've got to
  rewrite all the data files to freeze XIDs and, I don't know, zero out
  LSNs, or something.  And if you're going to rewrite all the data, then
  you've pretty much lost all the benefit of doing this in the first
  place. In fact, it might end up being slower than a dump and
  restore; even an uncompressed dump will be smaller than the on-disk
  footprint of the original database, and many dumps compress quite
  well.
  
  Robert Haas
  
  
  
  What about having database-level XIDs rather than cluster-level?  Is that
  remotely feasible?
  
  Thom Brown
  
  
  
  Maybe.  You'd need a set separate set for shared catalogs, too.  It
  seems like a heck of a lot of work, though, especially since (IME,
  anyway) most people only really one run one database per cluster.
  
  Robert Haas


Leaving aside all the internal implementation details / problems that would make this possible, the last comment has something that may be helpful to you: 

Run a different cluster per database. You would probably need to implement 
something of an infrastructure so when a user wants to "attach" a database, it would start up the related cluster and stop it when the user wants to "detach" it.