"There are a lot of people in Tokyo."
Yes, it is possible to use あります here, but I don't recommend this especially in beginner's course, because every case can be replaced with いる and it is very easy to misuse ある.
There are cases where ある can be used with animated subjects. One of them is when describing an ownership relation. Like this one, Tokyo has a lot of people. We can use ある to stress the ownership relation that Tokyo owns its people, instead of existence of the people.