I shall use another game, BZFlag, as a reference.
In it, you can drive using the keyboard, mouse, or joystick
and use the keyboard for any additional actions (such as dropping a flag during ctf)
When you press the chat button, the keyboard locks up, and you can only continue driving if you were using the mouse or joystick.
So you can type with one hand and drive with another.
In Spiral Knights, you can move using the keyboard or joystick (mouse is reserved for aiming)
aim using the keyboard (if aiming and moving keys are the same it's easier), mouse, or joystick (hat or alternate axes)
and use the keyboard for any additional actions (such as throwing a vial)
When you press the chat button, the keyboard, joystick, and mouse aiming lock up, and you can only continue moving and aiming after you are done typing.
So you can type or play.
Those whose steam has a game download for their operating system already have voice chat, and if they have microphones, can already communicate while playing.
I intend to learn to touch-type with one hand (without forgetting two-handed touch typing, probably through a mirror keyboard toggle), but such a skill is not currently useful with this game.
I ask that while the chat box is open, the game continues accepting gamepad and mouse input.
While this kind of option would be a good idea I don't think players would use it. Some players might but not everyone wants to learn to type with one hand when voice chat is much easier. Typing in almost any mmo is useless while fighting in a dungeon. If you stop to talk to someone the enemy is going to attack you and typing with one hand and fighting enemies can be difficult. Just switch to voice chat if you really want to explore the Clockworks and talk to friends during a battle without getting killed by enemies.