I print with mine without the stabilizing unit.
Mine came with a photodiode installed, so I measured this with an analog ohmmeter, through a small current limiting resistor. It also has a built in heater, so that over time the entire unit heats up.
What I found is that it takes about 20 seconds for the fluorescent bulb to heat up and reach peak intensity. After that there is a fairly long period of time with quite stable light output. Then after a few minutes it starts to change more quickly. After the head has been plugged in and in use for a while, it takes less and less time to reach that initial peak... eventually getting there in 5 or 10 seconds. But the important part is that the level of that peak is itself very stable.
Originally I was planning to hook up a permanent ohmmeter so that I could always begin exposures when the light is at the same level. I know there is at least one other person here at APUG who uses that approach. But I have not found that to be necessary, and I can make very repeatable prints, even weeks apart.
Before every exposure, I let the lamp warm up for 30 seconds. This is at least 10 seconds into the "stable" region. If I've been working for a while, I'll sometimes cut that back to 20 seconds, which should still leave a 10 second "safety factor". I use a dodging card and a metronome to make my exposures instead of a timer.... and now that "warm-up time" is part of my routine and I use it to think about what I'm doing, how I will dodge or burn, etc...
So, yes, it can, but if you want repeatable prints you'll need to account for that warm-up period in some way.
Edit: I see the "one other person" responded before I typed this

Edit2: Mainecoonmaniac is right, and my cold light is very blue. I mostly use split grade printing with a blue 47b and a green filter. There were later bulbs designed to work with VC filters but I don't have one of those.