Cool, you learn something new every day. But I still dont agree with you. Heres why:
"Now here is an interesting additional issue. What you mean by mass
depends on whether you are looking at a system from the inside or from
the outside. Imagine that the interaction that I described above took
place inside a large black box, and you are outside that box . If could
measure the mass of that box before and after the process you would get
the same answer. That is because any way you could determine that mass
would just be measuring the total energy that box contains (divided by c2). This
energy including the mass-energy and the kinetic energy of all the
objects (including photons) in the box, as well as any interaction
energy between these objects. As long as nothing enters or leaves the
box, that does not change, no matter what changes take place inside the
box!"
From
http://www2.slac.stanford.edu/vvc/faqs/faq5.html
Basically, if you weight the initial and final mass of everything involved in such a reaction as you so describe, you'll still end up with the same mass when the reaction ends.