switching out a heat/cool only thermostat to one with "auto" feature
Yes, the wires you describe are sufficient for an auto-changeover thermostat.  In fact, The Honeywell T8602D series already includes both an AUTO fan setting and an AUTO changeover setting.  See page 7 of the manual posted on the Honeywell website:

https://customer.honeywell.com/resources/techlit/TechLitDocuments/68-0000s/68-0164.pdf