Thank you for your thoughtful comments.

I agree that space needs to have a special functionality in certain places, i.e. in text input boxes. Still, there is a difference between a key functionality of the player being global with some reasonable exceptions, and being so heavily affected by application modality that users have to carefully place the application in a mode required by the application, to get what they want, done. 

"Furthermore, since text entries are part the the UI and need to be able to absorb spaces for their own functionality to work, it wouldn't be guaranteed to pause when you switch back anyway!"
This is a difficult question. In spotify, the search text box loses focus when you switch out of the app. Which is more important, rapid and reliable usage of the main function of the whole application, or important but nonetheless less often used search functionality? 

The one usage scenario where I would not want search boxes to lose focus when I switch out of the app is where I am confirming the name of an artist/album/song in say, a web browser, to be able to return to the music player to search for it in my collection. Then again, I am not sure if having to mouse back to the search box would be a great price to pay for having the main functionality work reliably. And again, just having to tab once to get the functionality working again (Amarok) is very different than having to tab through dozens of items to get it working.

But if there are buttons in the UI that you can tab through, should not tabbing to them and pressing space on them to activate be possible? In Spotify, the enter key serves this purpose. In Amarok and VLC, this appears impossible.

UI modality is usually a risk I want to avoid, unless I can make very sure that the mode and its consequences on what users can and can not do are clearly visible in the UI. Here, the modality is so strict and so invisible that it effectively renders the shortcut useless. 

It seems to me that ctrl-selecting more than one item with a keyboard is a marginal use case that few people except expert users would ever think of doing, whereas pressing space to play/pause is a near-global de facto convention across most music players. 

Usability is about usage context - what is reasonable in a file manager may not be reasonable for a music player. So even though there is a platform convention, if it makes little sense in a music player that in my opinion, the burden of proof should be on the person who thinks that the platform convention - not on the one preferring the "this is how music players generally work" design choice. Even GNOME all in all is a very small player in the real world. In my opinion, Jakob's law not only applies to web UIs!

'Jakob's Law of the Web User Experience states that "users spend most of their time on other websites."
This means that they form their expectations for your site based on what's commonly done on most other sites. If you deviate, your site will be harder to use and users will leave. ' http://www.useit.com/alertbox/9605.html (#8 Violating Design Conventions)

It seems that the reasonable way to do this research would be to see which players are the most popular on the market, and in cases like this where the UI detail is not a differentiating factor for Exaile, mimic their usual behaviour unless there is a sound reasoning not to. 

Some samples:
Spotify (over Wine): enter activates, space plays/pauses globally, except text input box. The only text input box (global search) loses focus when you switch out of spotify so space is guaranteed to play/pause when you return to the app.
VLC Player: in the main window and in the window where video is shown, space plays/pauses globally. In the playlist window, space appears to do nothing.
Amarok: enter activates, space plays/pauses globally, except search text input box. Search box does not lose focus when switching out of app.  

Maybe I'll fire upp Windows at some point and see how things work over there.