Is the net amount of CO2 sequestered by trees from the atmosphere simply related to the mass of new growth? My simplistic model for the carbon cycle was that plants (or trees in particular) photosynthesise and transpire. The former takes up $\small\mathsf{CO_2}$ and $\small\mathsf{H_2O}$ and the latter does the reverse but obviously not netting out. The carbon for the cellular material (in particular wood) comes entirely from atmospheric $\small\mathsf{CO_2}$ (?).

The mass of trees comes mainly from cellulose which is roughly 50% carbon. Therefore the mass of sequestered $\small\mathsf{CO_2}$ is simply related to the mass of trees, with the proportion equal to the ratio of the molecular masses of cellulose and $\small\mathsf{CO_2}$ with balanced carbon content. Wiki says cellulose is some sort of sugar type thing $\small\mathsf{(C_6H_{10}O_5)n}$ and carbon dioxide is obviously $\small\mathsf{CO_2}$ so the ratio is something like: for each kilo of tree/wood grows 1.62 kg of $\small\mathsf{CO_2}$ is sequestered?

Is this completely wide of the mark?
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.