In-universe, Alison and the Doctor (officially known as the Shalka Doctor) continued to have adventures, one of which is chronicled in the very first online-exclusive Doctor Who short story published on the BBC website, "The Feast of the Stone" (short story).
In the real world, "Scream of the Shalka" (webcast) was produced without knowledge that the BBC was about to recommission the live-action Doctor Who series in 2003. On the DVD release of "Shalka" the writer, Paul Cornell, states it would not have been produced if they'd known. When the TV series was announced, plans for more adventures of the Richard E. Grant version of the Doctor, with Alison, were cancelled. Christopher Eccleston was announced as playing the Ninth Doctor, and Grant's Doctor was basically stricken from the record.
This wiki does not enter into canon discussions, however the BBC has declared (by way of Eccleston being declared the Ninth Doctor) that Grant's Doctor, later dubbed the Shalka Doctor, is no longer considered an official Doctor. The only time he was officially referred to as the Ninth Doctor was in the reference book Doctor Who: The Legend by Justin Richards and published by BBC Books in 2003. In the book's second edition, Doctor Who: The Legend Continues, Eccleston was now listed as the Ninth Doctor.
An attempt has been made to reconcile the Shalka Doctor with continuity, as the novel "The Gallifrey Chronicles" (novel) suggests that three alternative "ninth selves" exist, referring to Eccleston, Grant and the spoof version of the Ninth Doctor played by Rowan Atkinson in "The Curse of Fatal Death". In truth, however, in the wake of "The Day of the Doctor" there are in fact four as John Hurt's War Doctor was another alternative Ninth Doctor.
It should be noted that Richard E. Grant's Doctor is never actually directly specified as being the Ninth Doctor in "Scream of the Shalka". Now that the Doctor has been given a new regeneration cycle in "The Time of the Doctor", it is conceivable that the "Shalka Doctor" could now be a future incarnation.