You probably could - blockchain.info has certainly taken steps towards letting you, and provide a reasonably complete API, along with websocket streams for real time data.

That said, you probably shouldn't - Bitcoin, and other cryptocurrencies, are designed to be decentralized and trustless. By using Blockchain.info, or any other API provider, you leave yourself open to a variety of attacks and issues. For example, how do you confirm that the tx data returned by an API provider is really the tx data on the blockchain? Most APIs do not provide any form of SPV support, so you can't request for inclusion proof.

Running a Bitcoin Node is a relatively low cost for a considerably higher security guarantee. I would strongly advise that you pull your data directly from your own node.