The net effect would be very small.
Although coffee provides some measure of stimulation, like many drugs the body becomes used to the effect. In fact, the net effect of regular caffeine intake is the the stimulant effect is largely negated. Caffeine is much more effective as a stimulant when it is used infrequently.
Caffeine withdrawal is rarely debilitating. OTC headache remedies are usually effective and often not needed anyway. Debilitating withdrawal symptoms are more common with heavy caffeine. Most caffeine users do not increase caffeine use far beyond common usage because of the increasingly dosage side effects of nervousness, restlessness, and sleep disorders.
Caffeine is also available from other sources (notably tea) and can be synthesized without particular difficulty. Though coffee is the source of caffeine used in soft drinks, etc. replacement by synthetic caffeine would not raise the price significantly. Bulk synthesis would certainly make the cost reasonable. It is rarely synthesized today as it is a by-product of the decaffeination process. Teas often have a higher concentration of caffeine than coffee, however since tea is usually brewed weaker, the coffee beverage is usually more potent.
A sudden destruction of the coffee crop worldwide would require an adjustment period and existing coffee inventory would have a large price increase. But there would not be much real difference in the real world after the adjustment period.
Starbucks would switch to overpriced tea. Worldwide more tea is produced than coffee anyway. We would likely get more creative in the ways we serve tea. There are several beverages that are considered coffee substitutes, but since Mrs. Olsen died in 1996 was there any doubt that the coffee apocalypse was overdue.
Clearly some individuals would have trouble adjusting, but most people would quickly adjust to the loss, and after a brief period of mourning, move on with their life. Adaptation - its part of what it means to be human.
I added some potentially interesting references as I see the skeptics version of this question has been put on hold.
Re: Caffeine withdrawal: ,
the incidence of headache was 50% and the incidence of clinically
significant distress or functional impairment was 13%. The threshold
of caffeine withdrawal was from doses as low as 100 mg/day
1 cup of coffee on the average has about 100 mg of caffeine.
Combining the fact the most debilitating withdrawal symptoms last from about 1 day to 9 days and the relatively low rate of impairment -- I believe it is categorically safe to say the any productivity issues would be a minor blip in the general population. Air traffic controllers, etc. may need to supplement with modafinil, etc. to maintain constant alertness.
Re: Caffeine tolerance
From studies on rats Separate groups of rats were given scheduled
access to drinking bottles containing plain tap water or a 0.1%
solution of caffeine. Daily drug intake averaged 60-75 mg/kg and
resulted in complete tolerance to caffeine-induced stimulation of
locomotor activity, which could not be surmounted by increasing the
dose of caffeine.