If one person sold bitcoins to another person using a smartphone, will a record of the IP addresses of the devices they used be seen in the blockchain?
No the blockchain does not contain IP addresses.
The bitcoin node or bitcoin API server (if used) that you initially send your transaction will know the IP though and they could keep it in their own databases.
For anonymous buying/selling you can use the Tor network. You may also be interested in mixing to anonymize bitcoin address (e.g. if you bought your bitcoins from an online exchange that has your IP plus much more).