In a wireless environment working with the 802.11 protocol suite, where the MAC protocol is based on CSMA-CA (collision avoidance), a higher data rate would mean that data is sent more quickly, which in turn implies that more number of packets are sent successively.
No. 802.11 allows different modulations, with more bits per symbol the better the S(I)NR gets. So, same number of packets is able to transport more data in a good signal scenario than under a bad signal condition.
Wouldn't a greater number of packets being sent mean a greater chance of collision?
Yes/No. Notice the Carrier Sense in CSMA. Admittedly, assuming stations are trying to access the channel more often, the likelihood of one missing the fact that the channel is currently used within a fixed duration becomes higher, but: Wifi cards (and drivers) are clever. They tend to adapt their MAC strategy (and: aggressiveness) to the occupancy of the channel.
as that entirely depends on how many packets are being transmitted 'over-the-air' at any point of time.
No. Not entirely. It also depends on how you sense, and what arbitration scheme is actually in effect.
Overall, I'm confused how high data rates would work well in a wireless environment, if it resulted in more number of collisions (which would be counter-productive).
Even with more collisions, you'd get more packets across – that's like saying "in a city with 100,000 cars, there's gotta be more traffic jam than in a city with 10,000 cars. I don't see how having 100,000 cars helps getting 100,000 people to work". Well, it does.