Using a preamp without a power amp

I feel a little silly asking this but I figure better safe than sorry... Here's my situation - I have a record player, a cd player and a headphone amp with only one set of inputs. I'm interested in a particular vacuum tubed preamp which has an excellent built in phono stage (also tubed). If I hook up my headphone amp to the preamps tape-out is it OK/safe to use it this way without having a power amp connected to the preamps main outputs? Also, assuming that this is allright, obviously my record player will benefit from the tubes in the phono stage but will the cd player benefit from the tubes in the pre? Are the tubes 'in the circuit' when the tape out is used and the pre's volume control bypassed? Of course I could just get a switchbox and a seperate tubed phono pre but I thought the pre would be a neat one box solution. Also, eventually I'd like to add a power amp & speakers. Thanks in advance for any insight.
You can safely use the main preamp outs to your headphone amp. And you can safely use the tape outs without anything connected to the main output.
Personally I would use the main output to a headphone amp. The tape output is almost certainly "buffered" and is not going to give you a better signal than the main out. Even though the main out is via the volume control!
As for the use/non-use of some of the tubes via the tape out, that is up to a manufacturer's design. If the pre has zero gain via the tape out, with the CD player connected, then, no gain is being produced, and perhaps the line tube gain stage is inactive (and only the phono tubes are actively engaged). If the tape out produces a louder signal than direct from the CD player out, then the pre does still have a gain stage in the circuit. (probably, this is not a certainty, as the impedance may be affecting things)
Thanks Elizabeth, your response is very clear and informative.
You would be better off using the main outs of the preamp due to the issue that running the preamp without any output can cause damage to some (many) preamps. You may want to check with your preamp manufacturer if you are at risk by not outputing the gained signal.