Aaron:
Any bad effect of oxidation is fairly insignificant, and then only on lignin. The chief danger when sinewing not-recently-surfaced wood is oil, especially from city air, deposited on the surface. Still, even in Bay Area air, I've never had a sinew to wood bonding problem, even on somewhat aged lumber surfaces. Still, if it's a concern, a very light scraping, or sanding as BowEd notes, fully eliminates any problem.
willie:
" Have you noticed any bowing due to shrinkage on your glue belly experiment? '
Sinew shrinks sideways and well as lengthwise. No problem on narrow thick limbs, but on wide thin limbs sinew shrinking sideways can concave the back, sometimes even cracking the belly. I've never had that happen but it's been reported.