Good question, as it hasn't been coded in as a main option, but wouldn't be hard to. There is however, a very straight forward way to add it, as a portal block.
1) Go into ACP
>> IMPortal >> Blocks Management. You will see a list of portal pages. Unfortunately mine is completely customised, and i can't remeber which one is the default one in XS - "3 columns" I suspect. In fact if you want you can go through the list - it will be the only page that has any blocks listed in it.
2) After selecting the age, you should be on blocks management page. At the bottom select "add blocks".
3) Add new block page:
(i)Give the new block a title, e.g. Shoutbox.
(ii) Block position - you'd want center here.
(iii) Set it to active, no caching, then from block file drop down list, select: shoutbox.
(iv) Choose view auth level i.e. whether you want unregistered visitors to see it (think carefully about that!) - nice thing about IMPortal is you can customise each individual block, even the permissions.
(v) Then select to display title bar and border (without it, it would look strange!).
4) All done. You should be back on the default page blocks administration page, so look for an entry for your newly created shoutbox - you can move it up and down to control where it comes out on the home page. Then go look at your home page.
I should add that it will contain the same text as the shoutbox on the forum page, because it only has a simple database table structure, i.e. nothing like the forum.