Pre-amp as input to another pre-amp?

I can't think of any reason it would not be safe. Turn the volume down on the Adcom to begin with and then turn it up as high as you need. I assume the Classe does not have tone controls, so here is no risk of accidentally doubling up on bass boost or anything like that.

...than connect tape out of your tape to the other preamp!

There is a tape out, but I was thinking of maybe using that for ... tape out.

Do people here think it will be safe to *try* this both ways? I would just hook it up both ways and see how it sounds, as long as I am not likely to do any damage at very low volume level.

Yes, but instead of using the pre-out on the tuner-preamp why not just use the tape out facility it probably has? Fixed output like your cd player, bypass the volume control of the first and probably sound better.