Alioop would be the best placed to respond to this given that she was present during the appeal (and is a verified expert) but I'll briefly respond in her absence
I wasn't present for the appeal and the media only report in snippets so it's difficult to contextualise the defence argument. However I think it's likely that arguing that Allison's death was accidental was a theory that was advanced so as to cast doubt over whether the requisite intent for a murder conviction was present, as opposed to an admission of any kind.
The defence is effectively having a little each way - Should the grounds of appeal that deal with the blood and the dumping of Allison's body fail (if upheld it's almost certain that this would lead either to acquittal or retrial), the defence have conceded that sufficient evidence exists to convict Gerard of killing Allison so they are putting forward a theory to the court which would suggest that one or more reasonable circumstances exist where Allison's death could have been accidental and therefore open the door for a possible downgrade to manslaughter.
In saying this, it is
possible that Gerard has made admissions to his legal team sometime after being convicted. The QCA can only take new evidence into account in very limited circumstances and this isn't one of them. The court may only consider new evidence if it wasn't available during the initial trial and if Gerard has made admissions obviously this evidence was available to be adduced at trial however he chose not to. If his defence team did in fact tell the court that he was responsible for her accidental death they would disregard this and reply something along the lines of "tell it to the High Court" (where such evidence may be considered).
Something to also take into account - In the event that Gerard did make admissions of some kind, while his defence team would be able to continue his appeal, the structure of their argument would have differed from what was apparently presented during the appeal. This is due to the narrowing scope of permitted trial conduct when counsel has been informed by the defendant that they are guilty of the allegation/s. Again I have to stress that I wasn't present so I could very well have missed vital "tells" but it's my opinion that it's unlikely that Gerard has confessed to anything. If he was to confess it would have been in his best interests to do so after the appeal was heard as the High Court is the only court with the power to act on such admissions (and even then only in very limited circumstances).
Only the opinion of someone who wasn't present and is not a verified expert on this board. I'm sure Alioop can expand when she is able.