It would depend on what is in your Paid Search Detection rules. If your paid search detection was set up to recognize a specific query parameter then it would have passed into the "Paid" report. If the search detection rules do not match the AdWord rules you are looking for, it would be in the natural report. If Adobe Analytics wasn't implemented on the website at the time and only GA coding was present, the data wouldn't be in the report. Paid Search Detection can be checked by going to Admin > Report Suites > select the report suite in question > Edit Settings > Paid Search Detection.
One thing you can do is pull a Data Warehouse report with 'referrer'. This will give you the full query string regardless of which report it was in for Analytics. If you know which query parameter you are looking for you could create a segment to look for specific referrer values. This will help you validate what is in the paid search detection report. For example: if my AdWord query parameter is 'qadword=' I would look for '?qadword=' in the referrer.
For more information on Paid Search Detection check out this article: adobe.ly/1TDnKUu