Chili peppers figure strongly in many cuisines that originate from the "Old World," such as Thai, Szechuan, Ethiopian, and Indian. Is there any history of what was used to add piquancy to recipes before the importation of hot peppers, or recipes that predate the Columbian exchange?
"Spiciness" is a somewhat vague term that includes different gustatory components. What you might be referring to is the "chili-heat" component, which is what people mean when they call a food "hot". Biologically, this is produced by stimulating a class of receptor-linked ion channels that are collectively termed TRPV.
Chili peppers have the chemical capsaicin that can directly stimulate TRPV receptors to produce the sensation of heat. However, many other chemicals can do the same thing.
In particular, black peppers (Piper nigrum) contains the compound piperine, which also stimulates exactly these same TRPV channels and also produces heat. Black pepper is indigenous to southern India, specially the Malabar coast, and has been used in India as a food item for at least 4,000 years.
So prior to the Columbian exchange, Indian food was given "pepper heat" by the use of black pepper and its close relatives long pepper (Piper longum) and cubeb pepper (Piper cubeba) which also originate in India. By around 2,000 years ago, they had spread through south east Asia, and some time later all the way up to southern China. So these places also have long history of using black pepper in their cuisines.
The heat of black pepper and chili peppers from the new world is identical in nature, since both stimulate the same class of ion channels. Capsaicin is somewhat stronger than piperine at stimulating the channels, but any dose-dependent effect can easily be compensated simply by adjusting the dosage (i.e., use more black pepper for more heat).
Getting back to where I started, "spiciness" is more than just heat. For that matter, not all "heat" is chili heat. There are other foodstuffs that people describe as "hot", for example mustard, horseradish, or even raw garlic. These foods produce their burning sensation through a related class of ion channels known as TRPA. These are old world products that existed in Asia prior to the Columbian exchange.
Spiciness also comes from actual spices, strong flavors like coriander, cumin, fenugreek, fennel, etc. So depending on exactly what you mean by "spicy", you may be referring to some of these tastes rather than chili peppers. They are all part of Indian and Thai cuisine.
So to answer your question, Indian food was plenty spicy even before the arrival of the chili pepper. However, since the chili pepper grows through all climate zones in India and is incredibly cheap compared to black pepper, it may certainly have made the chili-heat flavor more popular.