Did the introduction of New World crops really increase spice consumption in Indian cuisine?

Indian cuisine was spicy long before the Columbian exchange. There really aren't any herbs or spices from the New World that are used in Indian cuisine except for one: the chili pepper. But that one spice is immensely popular.

The chili pepper contributes "heat" to the food. Prior to its arrival in India, heat was provided by the black pepper (Piper nigrum) and the long pepper (Piper longum). Chili peppers arrived in India early in the 16th century, via the Portuguese to Goa. From Goa, they spread very quickly across the whole Indian subcontinent. The reasons for the rapid spread were that Indians were already accustomed to and loved "hot" foods, and because chili peppers being a tropical plant, could easily be grown throughout India.

It turns out that chili peppers can produce more heat more cheaply than black pepper. So these days chili peppers have replaced black pepper in many recipes. Black pepper is used more for its flavor as a constituent of garam masala or other spice mixes, while chili peppers tend to provide the raw heat.

Regarding other new world crops besides chili peppers, the ones that have made the most impact on Indian cuisine are potatoes, tomatoes, and corn. Potatoes are a staple vegetable across much of the world because they provide a lot of nourishment for the cost, and because their neutral taste can take on whatever flavors you choose from the spice/sauce mix. Corn was similarly adopted as a cheap grain - since the corn plant uses C4 photochemistry, it typically has higher yields than wheat. So in the wheat-eating parts of the country (north India), it was often used as a cheaper substitute for wheat in making bread (makke ki roti). This use has diminished since wheat yields increased after the green revolution.

Tomatoes are also widespread in Indian cuisine to provide tartness to the spice mix. Prior to the arrival of tomatoes (and in many recipes today), the same role was played by tamarind (imli) and green mango powder (amchoor). Again, like in the case of chili, while the ingredients have changed, the particular taste or flavor they provide approximates some other ingredient that was previously in use.

Peanuts are widely eaten in India, but they have not assumed the major importance they do in the US for example, where peanut products are found in a whole range of items from peanut butter to candy to ice cream. In India, peanuts are mostly eaten whole: roasted, with salt and spices added. They are more a snack than a staple.

Among other new world plants that could be considered "significant" in India today would be two fruits: guavas and papayas, which are widely eaten in different parts of India. Like the chili pepper, one reason why they flourish is because they are tropical plants and grow pretty much everywhere in India. In season, guavas are probably among the cheapest fruit you can buy.

There are other new world crops that are eaten in India, but don't figure prominently in Indian cuisine, such as cocoa/chocolate, vanilla, cashews, pineapple, etc.

You might be interested in this previous thread on Asian cuisines before the Columbian exchange.