Caffeine blocks adenosine receptors, thereby reducing the effect of adenaline.
It seems plausible to me, that blocking adenosine receptors should (perhaps ironically) increase the rate of adenosine buildup. For example because the body directly responds to a lower measured adenosine level by increasing adenosine production. or alternatively because coffee causes people to be more active, and this heightened activity may cause increased adenosine buildup.
Is my hypothesis correct?
Your question demonstrates a key understanding of homeostatic mechanisms: in many cases, long-term pharmaceutical modulation leads to compensatory changes that blunt the effects of the modulation. This can lead to rebound effects and sometimes physical/physiological dependence.
Your hypothesis is good, however, you have the mechanism wrong in this case. Blocking adenosine receptors tends to increase the expression of receptors, especially the adenosine A1 receptor, rather than the production of the agonist adenosine. Interestingly, this seems to be regulated not by increased transcription (mRNA production) but instead by later mechanisms (Johansson et al. 1993).
Receptor expression changes rather than agonist production changes tends to be a general rule for similar circumstances, though there are certainly exceptions as well. Altering receptor levels is a more reliable homeostatic mechanism, because often a given agonist acts on many different receptors with different affinities. It is also the cells expressing the receptors that have the most direct way to assay the level of receptor activation. In order to change agonist production levels, you would need a communication mechanism where the receptor cells signal back to the agonist producing cells, whereas receptor expression can be controlled all within the receptor cells.
References
Fredholm, B. B. (1982). Adenosine actions and adenosine receptors after 1 week treatment with caffeine. Acta Physiologica, 115(2), 283-286.
Johansson, B., Ahlberg, S., van der Ploeg, I., Brené, S., Lindefors, N., Persson, H., & Fredholm, B. B. (1993). Effect of long term caffeine treatment on A 1 and A 2 adenosine receptor binding and on mRNA levels in rat brain. Naunyn-Schmiedeberg's archives of pharmacology, 347(4), 407-414.
Ramkumar, V., Bumgarner, J. R., Jacobson, K. A., & Stiles, G. L. (1988). Multiple components of the A1 adenosine receptor-adenylate cyclase system are regulated in rat cerebral cortex by chronic caffeine ingestion. The Journal of clinical investigation, 82(1), 242-247.
Svenningsson, P., Nomikos, G. G., & Fredholm, B. B. (1999). The stimulatory action and the development of tolerance to caffeine is associated with alterations in gene expression in specific brain regions. Journal of Neuroscience, 19(10), 4011-4022.
