The simple answer is 'No'.
The signals which come via a satellite dish use different frequencies to those used by the Freeview service. (They also carry different programs and most of the signals are encrypted).
To get the Freeview box to work, you need a decent external TV aerial. The one most frequently recommended (and praised), here on AB, is this one:
http://www.maplin.co.uk/Search.aspx?criteria=p t18u&source=15&SD=Y
Your satellite dish can only be used to receive digital TV if it's connected to a Sky box (or similar equipment). A box without a 'FreeSat' card will only receive a limited number of stations, most of which are available on analogue TV anyway. (e.g. BBC1). If you've already got a Sky box, the cheapest way to get a wide range of digital channels is to purchase a Freesat card, from Sky, for �20. (If you've not got a box, you can buy one cheaply from eBay or from your local 'free ads' paper).
To learn more about Freeview (which is the service you'll get through your new box if you install a decent aerial), see here:
http://www.freeview.co.uk/home
To find out about FreeSat (which is a different service, available by using your dish, together with a suitable box and FreeSat card), see here:
http://www.freesatfromsky.com/
Chris