Hummm, from what I remember about battery chargers, they're neither CC nor CV, but have properties of both.
Anyway, they all have overcurrent limitation (which your welder does not in a CV mode, since its merely limited by the capacity of the machine, which is almost certainly over the charging limit of your batteries, unless maybe they're from a forklift), to prevent charging at too high a current.
Charging at too high a current will cause hydrogen gas to be generated by lead-acid batteries, and permanent battery damage.
My guess is that you can get away with this for a number of seconds, and a machine with true CV properties might make a decent jump starter, but you would really need to baby sit this like a boiling pot on the stove, to charge safely.
Dead lead-acid batteries are best charged in three steps.
The first step charges the battery up to 80% in a CC mode, and is kept at this current rate, until the battery voltage reaches 14.4V.
So, if you knew the voltage the batteries started at (say 9 each), and set your machine to that, and hooked it up.
Then, with an ammmeter (really important to do this with any degree of safety), you could keep increasing the voltage until the ammeter read the max charging current to simulate CC.
Then the battery is charged to 98% in a CV mode, at 14.4V, while the current will slowly decline.
Your machine will probably not be able to finish the battery off in the float mode.
Now that I wrote this, I noticed this great article found on google:
http://www.batteryuniversity.com/partone-13.htm