Not to any useful degree. If you wanted diffusion before, you'll still want it.

Full CTB cuts a lot of light (like 75% I think)
In most situations a 3/4 CTB will be enough to match the daylight.
I usually use 1/2 CTB only and white-balance to the daylight. This gives my lights a warm touch which is pretty nice and it leaves roughly enough light output (and I'm talking about 800W and 1k halogens...). Never underestimate the power of daylight, even if it's just a small window...

There are easier ways to get around these situations especially when time and budget is an issue. A lot depends on your schedule. Keep in minds that the outside light is unpredictable; it constantly changes and if you have a long shoot and consistency is important gels or no gels you might run into problems. Every year I do a dozen video projects for international resorts around the Caribbean and South America, I’ve been doing it for the last 20 years. These are good shoots but we don’t have the luxury to start gelling windows or travel with extensive equipment. For our interior shots we build our schedule around the existing light. There’s about an hour in the morning and another at night where the brightness of the outside light matches the interior light and also the color temperature gets very close thus requiring a minimum of gelling on the lights. This is the time that we do all the shots that must be blended with daylight and has been working very well for 20 years and hundreds of shoots.

Thanks a lot for all the great feedback :) .