While you may be eligible and apply to enter the UK under the Ancestry program, it is still a visa application process and you will need to provide quite a few documents, in addition to your current passport. These include birth certificates, yours and your parent(s) and grandparent(s) upon which your ancestry claim is based. In addition, you will be required to disclose previous UK travel history, both the working holiday programme and the overstay. So, yes, your history may have an affect on this application, as full and open disclosure is expected, and anything less can have negative impact.
You may want to consult with a UK solicitor in advance of application, one knowledgeable in immigration law (e.g., via Skype). These can be located through the Law Society search tool or the search option of the Immigration Law Practitioners’ Association.