That won't increase your signal strength - it's not an amplifier. All it does is carry power along the coaxial to power the dish switch. It's not meant for connection to any other devices - the 12V could potentially be harmful to them. The extra voltage is separated out after the switch.

But that won't increase your signal received by an antenna. I suppose it may be possible for it to trick a signal meter, but it's not going to improve your reception.

And yeah, that amplifier is not only amplifying the noise, but it's adding quite a bit of its own. That type of amplifier is meant for boosting already strong CATV signals for distribution (ie, to overcome splitting it many times), where noise is less of a concern. It's not surprising that it's detrimental to your reception here.

Your best bet is to get a decent preamp.