The problem is that DAB reception can vary significantly over fairly short distances. (Reception can be very different at two locations which are less than half a mile apart). Putting 'PO1 1AA' into the postcode finder shows all the stations, which I referred to, as being 'very likely' to be received. Even if someone living in Portsmouth answers this question, their experiences might not give an accurate indication of the reception conditions where your parents live.
If you take a look at the DAB coverage map, you'll see that the area around Portsmouth is made up of a mixture of 'yellow' and 'blue' areas. It seems that PO1 1AA must be in a yellow area, while your parents postcode must fall into a blue one. Even so, blue shading still means that at least 90% of addresses should be able to receive BBC digital stations, so the chances are quite high that your parents would be able to do so:
http://www.bbc.co.uk/digitalradio/listen/cover age.shtml
Chris