From personal experience, it can. It also depends on your definition of "hard". For me, if it rattles the entire car, and loud enough to almost bleed your ears, then yes it hits hard. If your purpose is to be a douche and piss your neighbors off from two blocks away, then no.
Also, it's not the wattage that "hits hard" it's the design of the box, design and the efficiency of the speaker. Yo!
Yes, in high school and college, I was that douche bag. Although I am still a douche bag, my douchiness now manifests itself in different ways. My car didn't rattle, though. I covered everything in DynaMat. I added neoprene to all contacting surfaces. If something rattled, I neoprene'd it or added rubber washers or added expanding cell foam.
Additionally, I would agree to your wattage statement to an extent. Ported boxes will hit harder, but won't sound as crisp and will be slower, duller. Comparing two ported boxes, a 250-watt setup will be much louder than an 80-watt setup. I image that an 80-watt sub would burp tremendously at high volumes.
A 250-watt sealed box would be perfect. Low battery drain will save your battery and your alternator. I had to install a beefier alternator. My original alternator died, replaced it under warranty, and it died again in 6 months. My performance alternator, roughly the size of 5 pounds of bulk beef, never died.