KN, yes it is analogous to optimizing the match between signal levels and the dynamic range of recording tape. The main difference, of course, being that a modest amount of analog tape oversaturation may still provide reasonable results, while any overload of digital recording equipment will produce very hard clipping.
There doesn't seem to be much meaningful technical information on the Grado headphone amplifiers. But assuming you are using the non-high gain version, that is intended for use with Grado headphones, unfortunately I suspect that its gain and output voltage capability are such that it would not provide enough voltage to fully utilize the dynamic range of the Linestreamer, when driven by a signal level corresponding to the output of a phono stage.
It appears that the high gain version was introduced for the purpose of driving non-Grado phones having impedances of 100 ohms or more, which require higher voltages than the 32 ohm Grado phones require, for a given amount of input power. And I did find some review comments indicating that the non-high gain version can't drive certain Sennheiser and other models to high volume levels. Finally, the fact that a similar model exists which runs on battery power, and is described as being able to run for 40 to 50 hours on two 9 volt batteries, would seem to indicate that the design is not particularly high powered.
All of that is speculative to some degree, of course, but the lack of technical specs on the amplifier precludes anything more definitive.
Regards,
-- Al