Short answer:
No, you won't get Alibi with a 'Freesat from Sky' card.
Long, boring answer:
There are two types of 'free' satellite channels, 'free-to-air' (FTA) and 'free-to-view' (FTV).
Any generic satellite receiver (which is what a Sky box without a valid card becomes) can get you all FTA channels. (There's a full list of all those channels on the Astra satellites that Sky uses here:
https://en.wikipedia.org/wiki/List_of_free-to-air_channels_at_28%C2%B0E ).
However FTV channels are encrypted meaning that, although there's no subscription to be paid in order to view them, you must have a valid viewing card in order to handle the necessary decryption.
At one time quite a few 'free' satellite channels used the FTV method of broadcasting, so there was some point in forking out £25 for a 'Freesat from Sky' card. However there are now hardly any left, so there's not much point in getting a card. Assuming Wikipedia to be up to date, the only extra channels you'd get would be Insight HD, Sony Movie Channel (and its +1 version) and Yesterday+1. Other than that the only benefits of a card would be to enable you to receive any local channels that might be available in your area, and to ensure that you got regional news and weather.
https://en.wikipedia.org/wiki/Freesat_from_Sky#Extra_channels
UKTV (which is jointly owned by the BBC and Discovery) offers some channels (such as Dave, Drama and Yesterday) free of charge by satellite (as well as through terrestrial Freeview), with advertising pay the costs of those channels. However their 'premium' channels (such as Eden and Alibi) can't be made to pay through advertising revenue alone, so they're ONLY available as subscription channels:
https://en.wikipedia.org/wiki/UKTV#Present