Is the net amount of CO2 sequestered by trees from the atmosphere simply related to the mass of new growth?
Simple answer: No. The process "carbon sequestration" considers the whole Earth system holistically (otherwise it would not serve its purpose), and in your case, you only look at the plant-atmosphere system so nothing can be said of the amount of carbon sequestered. 

What you are describing is more close to Net Primary Production, which is defined as carbon fixation from photosynthesis minus carbon released from autotrophic respiration (which is somewhat different from transpiration that you mentioned).

Carbon sequestration refers to the transfer of atmospheric carbon into a relatively stable pool of carbon (on a climate-relevant time scale, usually at least in decadal-scale). "New growth" implies all the biomass gains of the tree over time, not necessarily "stable" biomass only. One obvious case arises for deciduous trees where large portion of "gained" leaves fall and decompose relatively rapidly.