The risk comes with supplies with a crowbar overvoltage protector. The idea is that when powering sensitive transistors, you want to prevent voltage excursions caused by inductive kickbacks etc. since the transistors could be damaged. These types of supplies are often identified by an analog pot on the front panel that needs to be turned with a screwdriver, but they may take other forms. The crowbar circuit uses a triac or diac to short the output terminals if the voltage across them exceeds the set point, thus protecting the DUT from overvoltage damage. This type of supply should not be used to charge a battery.
From the circuit diagram I can't tell if that applies to your supply or not (does the "Voltage Control Circuit" include a triac?), but you can study the power supply for any method of setting the overvoltage level.