Right now no. All testimonials must be approved. I will consider adding that as an option in the future though.
I know it can be inconvenient, but do people want testimonials automatically showing up under that section without any form of moderations?
There is a lot of spam bots that hit WordPress sites. That's why this plugin offers integration with 2 different captcha systems and can even use Akismet. If none of these are enabled they will be subject to a lot of testimonials selling "ugg boots" and other spam that gets submitted.
If your client has a falling out with someone (not even necessarily a client), they can leave a nasty testimonial and it will show up for the world to see until your client takes it down.
Thanks for the complement about the plugin.