You ask two questions, (1) whether it is beneficial to think in a logically consistent manner, and (2) whether it is always beneficial to think in a logically consistent manner. To answer these, we have to take a look at two different aspects of thinking.
First aspect: Belief Systems
Regarding your beliefs, I would say the answers are Yes to (1) and No to (2). It is generally beneficial to have consistent beliefs and as a rational animal you strife to eliminate inconsistencies by further thinking, experimentation, belief revision, and so on. It would not be beneficial to always have consistent beliefs (and also not be possible, because people make mistakes), because you aggregate beliefs and form knowledge from various different sources: perception, your own thinking, and other people by testimony. At least for the latter, it is beneficial to keep track of possibly inconsistent information in order to evaluate it later. It would be harmful to immediately revise all your beliefs in light of contradicting evidence or ignore contradicting evidence in order to forcefully maintain a consistent belief system.
Second aspect: Drawing Inferences
Here again the answer is Yes to (1) and No to (2), but for different reasons. First of all, not all inferences are logical in the narrow sense of being 'deductive' (as in classical logic). You also need to make inductive inferences and possibly abductive inferences, where it must be mentioned that the existence and justificatory status of abduction is highly controversial. These are not logical in the narrow sense but the have been studied by philosophers, logicians, computer scientists and mathematicians in great detail, too. Secondly, there are general complexity considerations that speak against the view that one can or ought to always make perfect deductive or inductive inferences. With an increasing number of variables and background assumptions deductive and inductive inferences become computationally intractable. You'd be paralyzed by your inferential processes, which would take too much time to complete. Instead, humans make a lot of heuristic shortcuts, which only work sometimes and lead to erroneous results in other cases (cognitive biases). In computer programming, shortcuts are also used, or alternatively incorrect simplifying assumptions are made. (For example, for a Bayesian network to become tractable you need to make strong assumptions about the independence of random variables which are rarely fully justified.)
Bottomline: No, logical thinking is not always beneficial, but it is so most of the time - at least if time permits.