it is possible but in my opinion it is more comfortable to use metamask because doing tasks with a cellphone is very difficult, besides ethereum, trustwallet has many other chains such as binance chain and trustwallet can be used to store NFT to.
Yes, doing tasks on the mobile devices isn't as efficient and easily doable job than using a PC or a laptop on which you can have metamask installed with which you can easily do the tasks and earn the airdrop tokens, but airdrop hunting right now isn't as profitable as of 2015 and before where a decent airdrop could have easily landed you good amount of bitcoins, so it is better to work for bounties and then use those tokens.