Less so than with Slack.
a) If you're willing to accept using a SaaS for corporate communications, then Discord is no different than Slack. You run the risk that the vendor is recording what you do on the other end of that connection. For what it's worth, such a security stance also requires you to run your own email servers. The IT workload to run all of the above is extremely high, prohibitively so for startups and small companies. Even if, from a security perspective, it would be ideal to host it yourself - for most companies it's simply economically impractical.
b) Granted that you accept the risk of your vendor recording your communications, the odds of those communications being recorded are much, much lower for voice communications than they are for text communications, for the sheer cost of storing voice and video data. Running the audio through speech-to-text before discarding the audio may be a threat, but not for users whose office lingua franca is in a language not supported by contemporary speech-to-text tools, let alone automatically deciphering which language the users in a given voice channel are speaking without it being defined ahead of time.
In short, as long as you're not buying communication services from a competitor, you're probably fine.
By recorded I mean keeping a separate copy, i.e if somebody deletes a message or file in the UI then the malicious vendor doesn't delete their copy of the message or file. That's eminently more feasible for text communications as the costs of storage are so much smaller.
