I think whether reality checks make you more rational largely depends on what sorts of checks you are using. There are many checks that exploit "surface-level" features of dreams-- most commonly inconsistencies in clock faces and written text upon second looks-- in order to determine whether one is dreaming. These checks are useful for determining whether you're asleep but generally limited otherwise.

However, there is one somewhat deeper feature of dreams that IMO provides a more useful opportunity both for reality checks and for rationality practice. Dreams, by their very nature, lack a logical underpinning for events. We tend to find ourselves in the middle of a series of events without much explanation for how or why we arrived there.

Thus, one reality check that I find useful both in dreams and waking life is the thought "where am I, and how did I get here?" For instance, right now I am at my computer, typing a LessWrong post. I got here from waking up in my room and walking downstairs. I got to my room from driving my car after a party with friends last night.

Obviously, this type of reasoning can go on and on. The interesting part is that dreams lack this.

For instance, I recently dreamed that I was on an airplane. I thought to myself "How did I get on this airplane?" Realizing I had no memory of getting to the airport, I became lucid. You might wonder how this applies to rationality. The answer is that "Where am I and how did I get here" can easily apply not only to physical reality, but also to your mind and thoughts. Indeed, it is very similar to "What do you think you know, and how do you think you know it--" one of the classic questions of human rationality.

In my experience, internalizing the general form of this principle has been very useful both for dream checking and for improving rationality.