when looking at the "conversion" event, you can perform different breakdowns which would give different results based on your example:
"marketing channels": since "natural search" is allowed to override, your customer would be counted here. the initial channel "paid search" would be overwritten.
"tracking code": the customer would appear with the "sem-..." tracking code, since this was the last code he touched and it is within the expiration window
remark: you might want to use some of the new attribution models which have been added to adobe analytics recently. this way you can give credit to different marketing channels based on a model you prefer. look here for more information: Attribution IQ