No, there is no causal relationship between signing FTAs or even bilateral investment treaties and getting increases in your country's productivity or competitiveness or number of jobs or average real wages. It depends on what you do with the rest of your policy toolbox.
If you have the ability and the know-how to have effective policies to supplement an FTA or a BIT, then you might get those results. I think FTAs and BITs are instruments of policy that provide opportunities for those things to happen, but they are not sufficient elements or sufficient conditions for that to happen.
For example, you mentioned the case of Honduras. I very much disagree that Honduras will have the public policy capacity to benefit in a substantial manner.
What happens is, if you sign an FTA between country A and B, and A has a very capable toolbox of policy-makers and so on, it may benefit very much from the FTA, and country B may not because it doesn't have them. But FTA is sort of the easy part, or the BIT is sort of the easy part of it.