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With bass traps, it's all about coverage area and mass of absorptive material. The more of both you have, the more effective your bass traps will be. Simple as that.
So to answer your question, yes it will still absorb some, no it won't asborb as much as a 24" wide panel.
Eventually there is a point of diminishing returns, but there is a reason 24" wide is the de facto standard. Actually there are several; absorbing materials are commonly available in that width, and 24" is a good compromise between performance and space-taking-upedness room intrusion. :-)
If you must stick with 16" for space reasons, consider treating the wall/ceiling corners as well, preferably 24" wide but 16" wide if necessary.
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