No but something like a single-ended EL84 (e.g., the Maggotbox Magnavox AMP-196 chassis) would probably be OK. That said... the impedance on the secondaries on the output transformers are probably a little on the low side, and the power output is probably dangerously high for most headphones.
(borrowed image from an eBAY auction)
The headphone jacks on old vacuum tube amps/receivers from, e.g., Fisher, used resistors to manage the power output to the phones
and to keep the output transformers happy. Something like 125 ohms, if memory serves. EDIT: looks like ca. 355 ohms in the Fisher 500C receiver:
source:
https://www.quadesl.com/refurb/refurb_fisher500C.html
Dollar for dollar, one of the modern, inexpensive Chinese-made stereo tube headphone amps would probably be an all-around better choice for use with headphones, though, truth be told.