In fact, 54 percent of Americans over the age of 18 drink an average of 3.1 (8 oz) cups per day; the equivalent to 40 billion dollars spent solely on the ever-so-popular cup o' Joe. With over half of the American adult population sharing the same admiration for good ol' java, what's happening inside our bodies if we're drinking it every single day?
Edit: I realized there have been a very similar answer on Coffee SE, already. Excuse me for my lack of attention. I add this link before my answer to complete the discussion.
What's happening inside our bodies, is quite a question. I cannot answer that. However, I can answer the entitled question; no, you shouldn't be dehydrated by consuming coffee.
There are numerous studies made on this issue. Some of them including sports area some others are generic.
Scott Paluska states:
Caffeine is the most commonly consumed drug in the world, and athletes frequently use it as an ergogenic aid. It improves performance and endurance during prolonged, exhaustive exercise. To a lesser degree it also enhances short-term, high-intensity athletic performance. Caffeine improves concentration, reduces fatigue, and enhances alertness. Habitual intake does not diminish caffeine's ergogenic properties. Several mechanisms have been proposed to explain the physiologic effects of caffeine, but adenosine receptor antagonism most likely accounts for the primary mode of action. It is relatively safe and has no known negative performance effects, nor does it cause significant dehydration or electrolyte imbalance during exercise. Routine caffeine consumption may cause tolerance or dependence, and abrupt discontinuation produces irritability, mood shifts, headache, drowsiness, or fatigue. Major sport governing bodies ban excessive use of caffeine, but current monitoring techniques are inadequate, and ethical dilemmas persist regarding caffeine intake by athletes.
Paluska, S. A. (2003). Caffeine and exercise. Curr Sports Med Rep, 2(4), 213-9.
Yang Zhang et al. states:
In practical terms, there was no evidence that caffeine ingestion in moderation would impair fluid balance during prolonged exercise in the heat or during 3 hours of recovery.
Zhang, Y., Carter, S. J., Schumacker, R. E., Neggers, Y. H., Curtner-Smith, M. D., Richardson, M. T., ... & Bishop, P. A. (2014). Effect of caffeine ingestion on fluid balance during exercise in the heat and during recovery. South African Journal of Sports Medicine, 26(2), 43-47.
Sophie Killer et al. states:
It is often suggested that coffee causes dehydration and its consumption should be avoided or significantly reduced to maintain fluid balance. The aim of this study was to directly compare the effects of coffee consumption against water ingestion across a range of validated hydration assessment techniques. In a counterbalanced cross-over design, 50 male coffee drinkers (habitually consuming 3–6 cups per day) participated in two trials, each lasting three consecutive days. In addition to controlled physical activity, food and fluid intake, participants consumed either 4×200 mL of coffee containing 4 mg/kg caffeine (C) or water (W). Total body water (TBW) was calculated pre- and post-trial via ingestion of Deuterium Oxide. Urinary and haematological hydration markers were recorded daily in addition to nude body mass measurement (BM). Plasma was analysed for caffeine to confirm compliance. There were no significant changes in TBW from beginning to end of either trial and no differences between trials (51.5±1.4 vs. 51.4±1.3 kg, for C and W, respectively). No differences were observed between trials across any haematological markers or in 24 h urine volume (2409±660 vs. 2428±669 mL, for C and W, respectively), USG, osmolality or creatinine. Mean urinary Na+ excretion was higher in C than W (p = 0.02). No significant differences in BM were found between conditions, although a small progressive daily fall was observed within both trials (0.4±0.5 kg; p<0.05). Our data show that there were no significant differences across a wide range of haematological and urinary markers of hydration status between trials. These data suggest that coffee, when consumed in moderation by caffeine habituated males provides similar hydrating qualities to water.
Killer, S. C., Blannin, A. K., & Jeukendrup, A. E. (2014). No evidence of dehydration with moderate daily coffee intake: a counterbalanced cross-over study in a free-living population. PloS one, 9(1), e84154.
Adam Seal, et al. states:
The data indicate that caffeine intake of 6 mg kg−1 in the form of coffee can induce an acute diuretic effect, while 3 mg kg−1 do not disturb fluid balance in healthy casual coffee drinking adults at rest.
Seal, A. D., Bardis, C. N., Gavrieli, A., Grigorakis, P., Adams, J. D., Arnaoutis, G., ... & Kavouras, S. A. (2017). coffee with high but not low caffeine content augments Fluid and electrolyte excretion at rest. Frontiers in Nutrition, 4, 40.
The most interesting result here may be the last one as it suggests that you should avoid drinking a lot. 6 mg caffeine per kg may cause dehydration.
Actually, from this previous discussion we roughly know how much caffeine are there in a cup of coffee; around 160. This means, as a typical 80 kg male, if you don't consume 4 cups of coffee one after another, it should not be a problem. In a few hours, some of the caffeine should be metabolize so you can drink some more. But I don't know the pharmakinetics of caffeine. Maybe a pharmacologist may answer better. In which intervals should we drink the maximum amount of coffee and not to dehydrate?
It is known that coffee is diuretic but (in general) if you usually drink water 6-8 glasses per day (except doing sports etc) you'll be fine. Sometimes on planes during long flights is suggested to avoid caffeine as you can get a bit dehydrated due to air pressure inside cabin. Overall as our body is of 70% water, our cells, blood need it, muscles too in order to avoid fatigue, water is the best friend for our body so an extra glass or two won't hurt :-).