You don’t say when you were dismissed and for litigation purposes that may be significant since if you were dismissed before 5 April your dismissal will have been automatically unfair. Since you have been offered an appeal you would have 6 months from the date of dismissal to bring a tribunal claim should you wish to. More generally an employer must act reasonably in dismissing on the ground of capability and this means two things: following a fair procedure and that dismissal is reasonable in all the circumstances including in the light of relevant medical evidence.
It is possible, and not necessarily unfair, to dismiss an employee in their absence if, for example the employee simply fails to turn up to a dismissal meeting without any or any good reason. So if it was clear that the last absence review meeting was going to discuss dismissal and you failed to turn up you really only have yourself to blame. On the other hand if there was no indication that you might be dismissed at or following this meeting then to dismiss in those circumstances is clearly unfair. It’s not clear what medical evidence was available to your employer but if they did not have up to date medical evidence that too may render the dismissal unfair (assuming ‘capability’ here means sickness absence and not some other performance issue).
You should appeal if you want your job back. The question you need to ask is whether you feel that you would want to work for an employer who would treat you in such a cavalier manner as your question suggests. If you do then of course you should appeal. If you feel that trust and confidence has been destroyed then consider if re-employment is really what you want. Tactically you also need to consider this-at the moment, on the face of it, your employer has acted unfairly in dismissing you in the way they did and you would seem to have a pretty good chance of a successful unfair dismissal claim. If you decide not to appeal because you have been treated so poorly then you are unlikely to be criticised by a tribunal. However, if you appeal you give your employer an opportunity to correct their mistakes at dismissal stage and to follow a fair procedure thus weakening any claim you may have. So, I reiterate, only appeal if you really want your job back.