Yes and no.
Thoughtlessness, can mean the same thing as rashness, (a quick action, without much forethought), however it does not only mean a kind of carelessness, or instictive reaction. Rashness tends to do with the quality of the action itself (done very quickly, almost without thinking). It was an immediate reaction. However, thoughlessness, can mean one did something deliberately without caring about another person's feelings. It's can mean the same thing as heartless. So most people would use recklessness as a synonym for rashness, because thoughtlessness has an implied emotional meaning. It's just because people say "that was so thoughtless of him to do that." (he really doesn't care about others feelings). Instead, to describe an action undertaken without thought, people would right "without thinking." "Without thinking, he kicked the ball into the net." That makes it seem more like the action was taken "without thought." rather than thoughtlessness, which implies an emotional characteristic, where a person has less thought for others (less empathy).