I work in maritime, often alongside Indian counterparts who speak both English to me and Indian to their ship mates.
Yes, they do speak Indian just as fast. Yes, the way they speak English has a lot to do with the cadence of how they speak their native language.
As far as the flow goes, I've noticed that Indian does flow better than English just listening to it, but I don't know enough of it to make that observation with any credibility.
There is no "indian" languaje, there is a myriad of languajes spoken in india, what you might be refering to is hindi, which is very wildly spoken.
I have two indian friends that speak english with each other cause their native languajes are so different that they do no understand each other and one of then do no speak hindi.