It won't mean he will be found not guilty of all charges. The best he can hope for at this stage based on the evidence in the appeal is that the convictions are quashed and the case is sent back to the Crown Court for a retrial. So we would be back in the situation before he was tried - he would be neither guilty nor not guilty.
Note that what follows should is not intended to express any opinion on Harris' guilt or innocence.
The basis of the appeal is that one of the charges against him is, according to the defence, provably untrue in that he was not present at the time the alleged offence was committed. The argument is that, when hearing a number of cases together, the jury may decide all of them on the basis of the overall weight of evidence rather than considering each of them individually. In some cases the jury may be convinced to convict on all counts even when the individual cases, looked at in isolation, are quite weak. If the Court of Appeal accepts the evidence that Harris could not have committed one of the offences, the defence would argue that it makes his evidence that he was not present at the time of one of the other offences more credible and weakens the prosecution case on all the charges. If the Court of Appeal decides that one conviction is unsafe it would be normal to say that we cannot then rely on the safety of the other convictions. However, that is not enough to declare Harris not guilty of all charges.
Nothing is decided yet. The Court of Appeal may decide to do nothing, they may quash the conviction for this one offence and leave the rest intact (unlikely) or they may quash the whole lot and send it back for retrial.