No, putting a wifi extender where the signal is already crappy does not help you.
Putting it half way between where the signal is still good will work a little better.
In reality though wifi extenders are usually a very poor option. Not only is the hardware subpar but due to being a single radio device they split your bandwidth in half so if you start with 150mbps by the time the wifi signal reaches the extender it is say 70mbps speed it gets split in half to 35mbps output and by the time it ges to room it is even less.
The much much better option is to use powerline adapters. TPLink's AV1000 is pretty decent and usually the same price as the slower models.
No $10 device is going to make a difference for your situation