Yes, I have mixed episodes all the time where I'm depressed and racing. It's also possible to have dysphoric mania which is when you race like you have mania but none of the euphoria. It's all rage, irritation, agitation, and so on....

for me it's very volitile state and somewhat dangerous as that's when I am most likely to self-harm. I am in remission for suicidal thoughts but others have concerns about that in a mixed state as well.