Short answer: No. Explanation: Here, "shopping" is a verbal noun known as a gerund. Adjectives normally go before the noun the modify, so in "online shopping", "online" is an adjective. In the OP, "online" tells us how the verb is performed, so it's an adverb. Compare: "Eating too quickly is bad for your health." Note that we do not say "quick", as we need an adverb here.

adjective

"Online" in this case is more of an adjective

Online is an adjective as it describes the noun, which is shopping.