It’s specifically against the rules.
https://www.blizzard.com/en-gb/legal/08b946df-660a-40e4-a072-1fbde65173b1/blizzard-end-user-license-agreement
License Limitations . Blizzard may suspend or terminate your license to use the Platform, or parts, components and/or single features thereof, if you violate, or assist others in violating, the license limitations set forth below. You agree that you will not, in whole or in part or under any circumstances, do the following:
Cloud Computing : Use the Platform, including a Game, in connection with any unauthorized third-party “cloud computing” services, “cloud gaming” services, or any software or service designed to enable the unauthorized streaming or transmission of Game content from a third-party server to any device.