that's a good question as the code above gives varying results on the blog/index page. In short yes you can play any tracks on it including the playlist connected to the index page itself if there is one (ie if you're using a static page as the blog index and you've put a playlist on it).
If you want the playlist to be same for all pages then you just put the id number of the page that has the playlist you want to use in the put tag. so if the page id was 100 you'd write:
Page id's are visible on the page/post edit screens in the address bar where it says .php?post=
BUT for other single page/post pages on your site you'd also need to force the scripts using mp3j_addscripts() to get the player to show as if there was no playlist entered in that page's custom fields then the scripts won't be added by default like they are on the blog index (i'll prob make this possible from admin in future version). I hope that makes sense.
fyi using the put tag with empty brackets is like using the shortcode in that the shortcode does nothing if there are no tracks in the custom fields. An empty put tag behaves the same. This means on the blog index you get the following:
If put tag is placed before the wordpress post loop: the tag only sees the first post in the list, if there's no tracks in this post then no player will show.
If put tag is in the loop: player show's with first post that has playlist
If put tag is after the loop: the tag only sees last post on the list, again if no tracks then no player shows.
Using the Modes for the put tag 'first', 'feed', or an id, give you control of the playlist. and Leaving it empty leaves it up to the player to auto add if it sees a playlist.