Yes you can use the booster and it will boost the signal
If it is just a problem of wireless signal distance it will work, if it is more then just signal range then its like trying to fix choppy high pitched audio by turning the volume louder.
Also a repeater will increase range but at the cost of speed/perfomance. A booster has to split its bandwidth between talking to your wireless devices and talking to the router. Its bassically a middleman and adds the dealy of A->B then B->C instead of just being able to go A-> C.
Zyxell is not a very high end brand and most of their products are not that great (they do have a couple stand-alone modems that are good). I would suggest instead to put money into a good router that has better performance. Buffalo HP serries routers have built in amplifiers in them to output x4 more power then standard routers do, and it has dd-wrt firmware.
How big is your home?