I doubt it, but will check later on, I have them both. If the condensors had been interchangeable, then surely we'd have a lot of buzz about the later version Valoy II Anti Newton condensor being ok for the 1C. (one wouldn't need the 1C AN glass then)
Pstake has got it right that the 1C AN glass fits the Valoy II condensor. But I have the feeling the Valoy II condensor is a smaller unit.
I would not worry too much about the 1C condensor. If the enlarger has been well treated, the condensor should be ok. And even if it does have a little something, it doesn't mean you'd always see that on your prints, on the contrary. Just check the condensor well, wash it in warm water with dishwasher soap and a small soft sponge, rinse well. Dry it with soft and clean cloth. You can also ask the seller to do this.
The problem with many 1C condensors is that they have a very even, almost invisible, layer of dust on the top. But they're easy to remove and easy to clean.