In order for Caffeine to help stimulate hair growth, there must be enough caffeine applied to the hair follicles and it must remain in contact with the skin surrounding the hairs for about an hour.
The majority of shampoos containing caffeine do not contain enough caffeine to be effective.
And the shampooing habits of most people are such that they do not stay in the shower for an hour with the shampoo in their hair. Most people leave it on for about 1 minute...not 1 hour.
So using caffeinated shampoo is probably not going to work.
On the other hand, essential oils combined into a hair oil treatment that are infused with enough caffeine to be effective can be easily applied to the scalp and left on for an hour.
After doing a caffeine hair oil treatment for an hour, you can take a shower and rinse out the oil with any shampoo. This procedure will give far superior results than using a caffeinated shampoo for a minute or two.