Yes. Both the web/desktop app and the Android app allow you to insert a HEX color.
On the web/desktop app, conversation colors can be customized by going to Settings > Theme Settings. Colors of individual conservations can also be personalized by opening the conversation, then clicking the 3-dot menu on the top right and accessing Conversation Settings.
On the other hand, you can check this article for more information on customizing conversation colors on the Android app.