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Yes you will lose power.
The point of an aftermarket exhaust system is to open up the restrictive stock exhaust. The piping is much larger, generally has fewer and less drastic bends, and the muffler is less restrictive (hence the sound). A silencer, by design, blocks out much of the exhaust opening, letting much less sound escape. Unfortunately this also put s a damper on air flow.
I'd say go ahead and get the silencer. While you may simply negate the point of having purchased an exhaust while using it, you can simply remove it while at the track. It's actually what they're designed for- daily driven track cars whose owner's don't want the exhaust tickets.
And you'll still get the aggressive tone without the volume.
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