Does intentionally being aware of an emotion or thought pattern increase the incidence of that thought pattern? As a means of tracking and exerting control over my life and emotions, I've considered doing a daily log to measure various life metrics, like what time I got up, how much coffee I've drunk, and various emotions etc. 

One of the metrics I've considered measuring the prevalence of suicidal thoughts. 

But what's put me off this idea is thought that actively considering this question would lead to further ideation, and would be counterproductive over all. 

The question - does intentionally taking note of a particular thought, cause you to think that kind of thought more often? Are there any studies or related studies into this?
In general, theories of self-regulation, emotion regulation, psychoeducation, and many forms of therapy posit that, in one way or another, awareness of your emotions or thought patterns is largely adaptive.  

This is true because self-awareness facilitates self-regulation (broadly speaking). For example, being able to identify the emotion you're experiencing allows you to plan a course of action to regulate it (e.g., Kashdan, Barrett, &amp; McKnight, 2015).  If I become aware that I'm experiencing anger, then I know that I can modify my anger (up or down) by confronting the source of it (e.g., my friend who owes me money).  If I become aware of my sadness, then I know that I can down-regulate it by seeking social support.  And so on.

Similarly, promoting meta-cognitive awareness of thought patterns can reduce depressive and anxious symptoms (e.g., Papageorgiou &amp; Wells, 2001; Wells, 2009). This is true because it allows you to examine your beliefs about how you think (e.g., "Is the way I think positive or negative? Does it make me feel good or bad?").  And once you've determined how adaptive your thought patterns are, then you'll be able to determine whether you should promote, maintain, or prevent their recurrence. 

However, it's important to note that while self-awareness is necessary for better self-regulation, it is not sufficient.  Effective self-regulation also relies on your knowledge of, and ability to carry out, adaptive courses of action. For example, you've just identified your thought patterns as maladaptive, and now you want to downregulate those thoughts.  Toward this goal, you try to suppress them.  However, ironically, this strategy ends up spurring more of those thoughts (as predicted by ironic processes theory; Wegner, 1994).  So despite your awareness of your maladaptive thought patterns and your subsequent desire to decrease them, you've actually increased their incidence and made yourself feel worse.  Alternatively, you might have used more adaptive strategies like psychologically distancing yourself from your thoughts (e.g., Kross &amp; Ayduk, 2011), engaging in mindfulness (e.g., Deyo, Wilson, Ong, &amp; Koopman, 2009), reappraising the content of your thoughts (Beck, 2011), questioning your meta-cognitive beliefs (Wells, 2009), and other standard therapeutic and emotion-regulatory practices that would have more effectively modified your thought patterns.

So, overall, whether self-awareness increases or decreases the incidence of your thought patterns depends on your subsequent self-regulatory actions.