Hmm.
I'd never heard of the Elgato device, I don't use a Mac and I've not got Sky, so this took quite a bit of web searching. (i.e. I think I know what I'm talking about about I'm not giving any guarantees!).
Just for the moment, forget about the Sky box. The Elgato dongle incorporates a Freeview tuner so, as long as there's a suitable aerial attached (either the one which comes with it - if the signal's strong enough - or a rooftop aerial), you should be able to receive all of the Freeview channels:
http://www.freeview.co.uk/channels/?lv[0]=chan nels
The Elgato dongle doesn't incorporate a satellite tuner, so it can't be used directly (even with a satellite dish) to receive
satellite stations.
Now we can consider the Sky box. This contains a single satellite tuner so, irrespective of whatever else you connect it to, you can't use it to view two different channels (or watch one channel while recording another) simultaneously. However,