Will a debt that has been purged from equifax and Trans UNion show up on an ERC?

Unlikely, but possible. An Enhanced Reliability Check could be more thorough.

However, any thing that old is less likely to be a disqualifying factor. The most important thing is that you do not omit information on the questionnaire you fill out. If you do and they find out, your failure to be completely honest would probably be viewed as a more serious act.

If there is a time frame on the questionnaire, you would not need to mention anything earlier than the period they require info on.