Though the quality of available evidence is not great, several reviews of deductive and inductive logic training programs do concur that studying logic can translate to improved logical reasoning (Klauer & Meiser, 2007; Nisbett, 1993; Hatcher, 1999; Perkins & Salomon, 1989; Baron, 2008 - pp42-44). However, purely formal logic training is not typically effective (Inglis & Attridge, 2016). Rather, training programs incorporating informal logic and real-world examples, are more likely to transfer to general logical reasoning skills.
Additional constraints on the effectiveness of logic training include:
- Teaching subject matter to an appropriate audience - ie, old enough, competent enough, sufficiently experienced, etc.
- Selecting effective subject matter for generalization - eg, language syllogisms, common biases, pragmatic schemas, etc.
- An adequate classroom environment - eg, social interactions, competent teacher, self-learning opportunities, etc. Modern approaches often incorporate software tools (Astleitner, 2002).
- Evaluating results using appropriate measures - eg, domain-general questions, real-world examples, validated tests, etc.
This question is part of a larger debate about how much learned skills generalize to other domains - known as the theory of formal discipline and transfer of learning. It is also part of a question about how best to teach critical thinking skills more broadly, of which logical reasoning is a component.
The study cited in the question - Attridge, Aberdein, & Inglis (2016) - does indeed test whether a course in logic improves logical reasoning. It also includes a brief review of some previous attempts. The experimental design uses a controlled trial method, but notably, it is not a randomized controlled trial (RCT), limiting the definitiveness of its conclusions. It does suggest that prior experience, as well as the measure used, affect the results of training.
As a general heuristic, I would not update too much on a single study anyhow, and always prefer to look for tertiary sources (textbook, encyclopedia) or secondary sources (literature review, meta-analysis) over primary sources (experimental study, theoretical work).