The value of formal instruction in critical thinking surely depends entirely on what type of person you already are. So having said one shouldn't generalize too much, I am simply going to do so, and let you filter my advice through your experience. Don't take my negativity as anything too much of an absolute.
As someone who has studied and taught math between career changes in computing, I am highly skeptical that introductory-level courses generally meet the needs of people with real-life experience unless that instruction directly addresses problems met in real life from some remedial angle.
I buy the Montessorian model of a skill as abstracted from applications in which one finds value. This applies to everyone, but especially to those not of 'school-age', including very young children, resistant teens, and full adults who have already done real work in the world. Unless there is some real barrier to getting on with the things you want to accomplish, the skills you need to accomplish them will arise naturally from use, and should not be programmatically taught.
Formal modes of thinking critically are closely related to language, and most things linguistic are surely best learned by example, and not by rule. But the best examples are not available in a general course in logic, or in a course intended to inculcate habits of logic. They are found in real solutions to real problems.
If you have trouble following philosophical arguments in general, or you are tripped up by the subtlety of the logic involved, it might pay to study Logic per se. But it might pay more to study formal linguistics, or to focus on the grammar of some very subtle language, or to study a highly self-critical mathematical discipline -- either math itself, or a modern science. Or, alas, it might pay most to simply trudge through the philosophy and discuss it until it coalesces into something you can 'get'.
Introductory courses intended to teach a specific kind of abstract still, instead of a real applied discipline, strike me as an unwarranted form of remedial education. They are assuming you need 'a grounding' in something that is usually discovered naturally at the point of application.