Do figures with no keywords (like Impossible Man) cause a team not to be themed?

From a Keyword standpoint and the game benefits that keywordered theme teams provide, yes. However, theme teams encompass more than those that share keywords or team symbols/abilities.

A themed teme needs all characters to share a single keyword. If one character has no keywords, it would break the theme. The team would not be considered a theme team.

FYI You can include Bystanders in your team and it will still be a theme team.

In order to be a themed team, all characters (except bystanders) on a force must share a keyword before the beginning of the game.

By default, including a non-bystander character with no keywords will prevent a force from being a themed team.

Note that there are ways to add keywords to characters when you build your force (potentially allowing a character that would otherwise have no keywords to be part of a themed team).