Diane,
Sure, it's possible. The phosphors in a picture tube are not entirely unlike those in a fluorescent lamp. However, the amount of light coming from the tube is very small, and it likely that a very strong portion is well out of range for pt/pd. If you left a sheet in front of one for an hour, I expect it would fog a bit.
You can try a fog test to see if it does. Cover a portion of a strip of coated paper with some cardboard or rubylith to use as a control and leave it for 30 minutes or so. Run it through the developer, and then clear it. It should be apparent if the light causes any fogging when you clear it, as the control area should clear completly, assuming you have fresh FO. The exposed area will show up as a faint graying of the paper in the coated area. Make sure you look at it in good room light to see if there is any fogging.
---Michael