It is important to not confuse First and Business class. Delta has First class on domestic flights and some short international flights mostly in North America, the Caribbean, and northern Latin America.
Business class is Delta One and features lay-flat seats and upgraded catering. It is featured on long-haul international flights and premium transcontinental flights. All flights with First class feature complimentary upgrades. No flights with Delta One (business class) feature complimentary upgrades.
There is an important distinction regarding Comfort+ between domestic and international flights.
For domestic flights (and international flights served with Delta's domestic First class) Comfort+ is treated as its own fare class, W. Therefore you are placed on an upgrade list as FO or GM or upgraded instantly after purchase as PM or DM to WU. There must technically be WU inventory available, but there almost always is. This applies for the Medallion and one companion, who must be at least a SkyMiles member, on the same PNR.
For all other international flights Comfort+ is treated as a purchasable seat selection. There is no "upgrade" since there is no fare class change. Sky Miles members can pay money to select C+, FO can select for free 24 hours from departure, GM can select for free 72 hours from departure, and PM and DM can select for free during or after booking. There are no inventory controls as there is no separate fare inventory. All Medallions are allowed to select a seat for themselves and one companion who must be at least a SkyMiles member.
Note: There has been a change today regarding which tickets are eligible for companion upgrades. Short answer, pretty much all.
Discussion here.