The usability downsides are quite apparent (to me):

• Toolwindow is usually quite small (in terms of vertical space) - unless you want to keep resizing it
• When query execution results show up, the small space is additionally partitioned into two regions: query and results. Both now have to share the already small space of the bottom-docked toolwindow, and I have to resize again to get a usable arrangement...

So while I'm actually trying to focus on a single task (editing the query), I'm forced to use only a very small fraction of the available screen real-estate.
This feels clumsy, especially for longer queries. (By the way, the "SQL Query" plugin suffers from the same usability problem)

For next IDEA version some big improvements should be within easy reach:

• The user is accustomed to editing text in the "upper"/"editor" area. Support this, by hosting HQL console as a regular editor tab
  • When I minimize all other toolwindows I now only see the query text. Good.
  • Tab title could show the Datasource I'm connected to. Useful to prevent common mistake of mutating or analyzing data on the wrong database.
• Query results could be implemented as a regular toolwindow.
  • Query execution would pop up this window, and I can quickly close it again (using Shift-Esc or Ctrl-Alt-F12) when I'm done looking at the results

It seems like the suggested UI would quite closely resemble Microsoft Query Analyzer and other database tools.
To me this indicates that the suggestion is a good one, since those tools have had many years to develop an effective user interface.