While it does not explicitly state that, it does say:
"(ii) copy, adapt, modify, prepare derivative works based upon, distribute, license, sell, transfer, publicly display, publicly perform, transmit, stream, broadcast, attempt to discover any source code, reverse engineer, decompile, disassemble, or otherwise exploit the Service or any portion of the Service, except as expressly permitted in these Terms;" [1]
Given that the API is not public if you are not using a bot key, I would think that using it with a third party client would take some form of reverse engineering.
The devs also stated that other client modifications like betterDiscord are against the TOS.
"(ii) copy, adapt, modify, prepare derivative works based upon, distribute, license, sell, transfer, publicly display, publicly perform, transmit, stream, broadcast, attempt to discover any source code, reverse engineer, decompile, disassemble, or otherwise exploit the Service or any portion of the Service, except as expressly permitted in these Terms;" [1]
Given that the API is not public if you are not using a bot key, I would think that using it with a third party client would take some form of reverse engineering.
The devs also stated that other client modifications like betterDiscord are against the TOS.
[1]https://discord.com/terms (Under Right To Use The Service)