That's exactly how I used mine -- see my signature line below.
The combo of BeePre, Kaiju and LCD4 is to my ears excellent. It would, however, be insane overkill for easier to drive headphones.
I started with Stereomour II, both in stock 2A3 form and as modded for the 45. The 45 was my favorite of the two, partly b/c it went lower in the bass and b/c strangely enough it sounded louder and punchier than the 2A3, despite having roughly half the 2A3's power (I've since scome across a theory that this apparent loudness may in fact be an effect of how the brain interprets 2nd harmonic distortion). Both sounded great, but I noticed that they could get a bit flabby and congested (loss of punch and clarity) with really demanding music (orchestral or even some pop/rock songs -- e.g., Rush's "Tom Sawyer" and Paul Simon's "The Obvious Child").
Going to the Kaiju wired for 16 ohms nominal output impedance almost entirely solved the congestion issue. And the Kaiju has amazing clarity and full, well balanced bandwidth and a nice, wide soundstage. Even with the stock caps, and no burn in, it sounded clearly superior to me from the very first listen. And then only got better. I think most, but not all, of that is from the Kaiju iron. It is a major step up from the Stereomour iron. I know this b/c I have since installed the Kaiju iron (chokes and output transformers) in my 45-Stereomour: it sounds great, but still noticeably short of the Kaiju. So I think the 5670 driver tubes have something to do with it -- and possibly the fact that while my Stereomours and Kaiju all have DC filament supplies (necessary for use with headphones, unless you can tolerate background hum), the Kaiju has a regulated filament supply versus the SII's unregulated one. I can also opine based on experience that it costs a lot of money to improve on the Kaiju iron - it is very very good.
cheers, Derek