Inexpensive headphone amp paired with an audiophile integrated amp

When one's integrated amp doesn't have a headphone jack and one routes out to a headphone amp, is the quality of the signal compromised by an inexpensive headphone amp?
If the headphone amp has a proper line-level input circuit with appropriate input impedance (say 10K ohms or higher), it will not affect the sound quality of the integrated amp when playing the speakers. Schiit makes some good headphone amps that meet these specs -- the Fulla at $99 and the Asgard at $199 are good examples.
Thanks. I actually have a Schiit Magna sending to Shure 1840 headphones from a nice musical fidelity integrated—as of yesterday. I just have no frame of reference to know if this makes good sense.
I have a Magni. The Vali with the right tube sounds much better.  
My xDuoo with two right tubes is even better.
Balanced in and out.