Firstly, it is important to remember that Flux Balance Analysis computes theoretical performance limits, i.e, the theoretically optimal behaviour of the system with respect to the objective and constraints. When growing bacterial cells growing in culture evolve under selection pressure for biomass production, the theoretical limit on biomass production may indeed be approached, see for example Ibarra et al: Nature. 2002 Nov 14;420(6912):186-9. (http://www.ncbi.nlm.nih.gov/pubmed/12432395) and Fong & Palsson: Nat Genet. 2004 Oct;36(10):1056-8 (http://www.ncbi.nlm.nih.gov/pubmed/15448692).
How closely other systems can be expected to approach optimality should be considered on a case-by-case basis, and the constraints should be realistic. In humans, you would for example expect that the physiology of the persons (blood glucose levels, etc.) would greatly affect the growth rate of any cancer cells, in addition to the structure of the tumour (especially blood supply). For cells growing freely in culture, one might expect FBA to be easier to apply.
For HeLa cells growing in culture, the results of at least one study suggests agreement between experimental and FBA-predicted growth rates: See Resendis-Antonio et al: Modeling core metabolism in cancer cells: surveying the topology underlying the Warburg effect. PLoS ONE, 5 (2010), pp. 1–11 (http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0012383)
Whether the precise biomass production rate is predicted or not may actually not be so important, and there has been considerable interest in applying FBA to studying various aspects of cancer metabolism. Here are some papers that may be of interest:
Ashwini Kumar Sharmaa, Rainer König. Metabolic network modeling approaches for investigating the “hungry cancer”. Seminars in Cancer Biology 23:4,2013, 227–234 (http://www.sciencedirect.com/science/article/pii/S1044579X13000436) (Review)
Shlomi et al.: Genome-Scale Metabolic Modeling Elucidates the Role of Proliferative Adaptation in Causing the Warburg Effect. PLoS Coputational Biology 2011 (http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.1002018).
Lewis & Abdel-Haleem. The evolution of genome-scale models of cancer metabolism. Front. Physiol., September 2013 (http://www.frontiersin.org/Journal/10.3389/fphys.2013.00237/full). (Review)
And a relevant Master's thesis: Computational Metabolic Modeling of
Cellular Growth: From Bacteria to Cancer. http://www.cs.tau.ac.il/thesis/thesis/Benyamini.pdf