Karin, it is possible, but not really.
Reasons are this:- when enlarging you sometimes need to have the enlarger light on for something like 10.4 seconds and the light has to extinguish very quickly. As a result, we normally use tungsten globes, which power up in a fraction of a second, and power down at about the same rate.
There are some enlargers that use a type of fluorescent tube as a light source, but these enlargers have the lights on all of the time and there is a large shutter in the head, which opens and closes, just like on a camera lens.
LED light source would (I think) be a possible light source for B&W enlarging.
If you wished to to contact printing with long exposures, say around 15 seconds or longer, then it is possible that you could use a fluorescent light source, either spiral tube type, or a straight normal one.
Longer exposures would make it easier for you to control the power up and power down time, but you would require the instant type of fluorescent tube for this to be reasonably practical, I would suggest.
There is also the impractical side of fluorescent lights in that they retain a glow after being switched off. To test this, sit in a room with your eyes covered and a fluorescent light on, turn the light off, open your eyes and you should see a glow from the fluorescent tube. This is bad for your B&W paper.